You can't just assume that 99% of the watermelon's "content" is the same as 99% of its weight. I don't know why they keep making their questions' wording difficult to understand.
it doesn't say 'watermelon content' - it says 'water content,' which is a phrase we use to express the mass of water as a percentage of an object or substances _total weight._ the question explicitly tells you that 99% of the total 100kg is water.
Not quite. Like this: ❌ Boss, I sleep only 98% of the time on the job now, instead of 99%! ✅ Boss, I doubled the amount of work I complete every day, I need a pay raise! 💸
@@HxTurtle yeah, more like "I'm doing less than half the work but only lost 1% of performance, yikes!" followed by "but why do you let me go with such good stats? Lost trust? How am I not dependable enough to not assign those tasks?"
@@kubastachu9860 eh a clearer explanation is assuming that the workload halved from 100 tasks to 50, and they went from doing 99 / 100 tasks to doing 49 / 50 tasks. their total task count has to change for this to make any sense.
That's not an equal comparison. In your scenario, your performance went from 0% to 50%, increasing by 10% each time. If you calculated it based on each task's percentage of the total remaining, it would steadily increase. For example; completing 1 task out of 10 is 10%, but completing 1 task out of 9 would be 11.111%, etc. When you reached 2 tasks remaining, completing one of them could be stated as completing 50% of the remaining tasks, but you'd still have only increased by 10% for each completed task when compared to the original list of 10.
The false assumption is that there is a 1% loss of water versus the original weight, when in fact it is only a ratio. Using that it becomes easier to understand that youre trying then to work out what weight fits the new ratio rather than thinking of it as having lost 1% of water
Yup, once understanding this, the problem becomes much more simple and obvious. Took me some time though because it's worded(quite well) to lead you to believe the % is not a ratio but rather an ammount
I knew it felt like I was missing something when it first thought about it. Which is why I was sure you would have to solve algebraically to get it but it's such an easy assumption and mistakes to make if you just read it
Somebody is cheating here with the wording! I could have sworn the video said 99% of the total weight (100kg) was water.... Or is that what the listener just infers themselves, hence the riddle? It just sounds like the person removed 1.01% of the total weight...
It's not a "false assumption". It's an incorrectly specified problem. And that's the real answer: "As specified, this question is too ambiguous to solve".
"dropped to 98%" means what? Is there an actual 1kg watermelon anywhere in the world such that, upon extracting 1% of its water content, its weight magically drops to 50% of its original weight?
Your method is far more intuitive to me than the ones Presh started with. First notice that 1%, hence 1 kg, is not water. For 98% water, we ask: “1 kg is 2% of what?” This question gives the intuitive answer 50 kg, or can be translated into the equation 1 = .02x, and hence x = 50 kg.
@@theglobalwarming6081 'I am both confused how much weight was lost ' Realize, there's an easier way to see the reduction in weight, take it further. 1kg solid and 99kg water gets the 99% water content. But to get to 50% water content, you have to have the starting 1kg solid, and only 1kg water left. You have to lose 98kg of the initial 99kg to get down to 50% water content. The water content percentage being referenced to the 1kg solids instead of an independent reference means the scale slides, and by using 1%/99% to start, the scale slides very hard. 99 kg of water is 26.12137 gallons. Take five 5 gallon buckets of water and another gallon, put them together, and try to wrap it all and hold it together with only 1kg of watermelon skin and rind. It's a not real problem, specifically chosen to use the self referencing 'water content' with an unrealistically high water content to generate the huge swing in values. It could work in some less familiar things, but you would be hard pressed to do this with a watermelon. Real watermelons tend to be 4% or so solid, they'll be mush before you get to 1%.
That's pretty much what I did. The water is the thing that changes and it's the unknown. But the mass of everything else is the same before and after. You start with 100kg total, 99% of which is water. So everything else is 1kg. The amount after, is still 1kg. You are told that the water content drops to 98%. So that means the percent of everything else is 2% Knowing that the amount of everything but the water is 1kg, and that the percentage of it is 2% , you can then calculate the total mass of everything as 1kg/0.02 = 50kg
@@ModelLightsfrom what I'm reading, watermelons are 92% water. Perhaps if you remove the inedible green rind then the editable red stuff is 96% water...
You focused on what WASN'T water, yet the water is the focus of the question (all the information is in terms of it). People think "oh 99% to 98% isn't much loss", and that's where they get tripped up.
I'm a maths teacher, and I think the problem here is in the application. There has been a movement ( a good one in theory ) to teach maths in context as much as possible, as this makes it more engaging, easier to understand and more valuable. Hence a question about watermelons instead of just algebraic questions. But if you're going to write a contextualised question, you are signalling to the reader/solver that it makes sense in the real world. So they will expect the answer to be somewhere within the realms of predictability. If one were to guess, no maths involved, how much the watermelons would reduce, one might expect an answer in the realm of a few kilos, so their expectation would confirm the mathematically wrong answer. The mathematically correct answer here is absurd in real world terms. So, don't bother contextualising the question in the real world if it doesn't actually make any sense in the real world. This goes for any question like, "Little Johnny is trying to find the ratio of white flowers to yellow flowers in the meadow by his house" or whatever ridiculous scenario. There has never been a little johnny who wanted to work that out. This is not a real world example. Has never happened. Will never happen. Try harder or don't bother!
Not at all. You can still make watermelon skin jam from it, and the concentrated watermelon juice can be drinkable. If it is not some kind of maidenless pit free melon, you can plant the seeds next year. Unless it also rotted. That would leave you with making some watermelon wine or vinegar at best.
This problem is solvable only if you assume that when you say something is 99% water, you mean 99% by weight. However, that is a false assumption. Most people, when they are told something is 99% water, they take that to mean that the volume of the said object is 99% water. Thus you have here two unknowns, you don't know how much the water weighs, and neither do you know the weight of the vegetable component of the watermelon. Therefore, this problem is unsolvable.
Thank you, this is exactly why I concluded the problem is unsolvable. The stated solution makes a big jump from "the water content is 99%" means that "the water weighs 99 kg".
It is safe to assume 1 liter of water weighs 1 kg more or less, depending on you location on earth, the temperature and how pure it is and such but that really feels out of scope of this riddle.. :)
This doesn't make sense to me, 1ltr of water is 1kg, so 99% of 100kg is 99kg which is equal to 99ltr. So 98% of 99 is 97.02, the 1kg dry weight doesnt change so the answer should be 98.02kg. I know I must be wrong but I just dont understand why.
If the non-water content goes from 1 (1% of the original mass) to 2% of the new mass it means that we lost half of the original mass. If 1 kg now is 2% the new mass is 50 kg.
The way I'd explain it is that while a drop from 99% to 98% might seem minuscule, the relative dry weight has doubled from 1/100 to 2/100, or 1/50. And as the dry weight hasn't changed, then it can only mean the total weight has halved.
if you're going to discuss these puzzles as more than "bar tricks", you really should eliminate errors like 1) MASS is not WEIGHT 2) % of total is given in terms of MASS or VOLUME
In the Netherlands this problem was presented about 20 years ago on a national IQ test TV show as a stallholder selling 200kg of cucumbers on a hot day. I remember being stunned by the answer as it is so counter intuitive.
To be honest, a "potato" containing 99% or even "only" 98% of water wouldn't be much of a potato. Even watermelons, according to Auntie Google, don't consist of 99% water. The figures I found on the quick was 92% water in a watermelon, and 80% in a potato.
simple explanation: assuming the non-water part of the melons didnt change, that part is still 1kg. that 1kg is now 2% of the total mass, or 1/50th, meaning the rest is 49/50ths, or 49kgs.
I think one reason for the confusion by many people is because they (like I did initially) interpret the "water content" as a percentage of the VOLUME instead of the WEIGHT. I pictured watermelon-shaped containers 99% full of water changing to 98% full of water, which is a different problem. :P
@@LLlAMnYP if it's just a single percent drop in volume, there is no guarantee it would equate to 50kg, or 40kg or 37kg, or anything, because we don't know what the volume to weight ratio is. This was my problem too, and couldn't seem to solve the equation this way.
To be fair, the question does not mention that the dry weight remains the same during the journey, so we can come up with any numbers for the answer, as long as the water content is 98%.
The better way to think about it to use units that are invariable rather than units that are variable. Water content is variable, so let’s rephrase it into ruffage content (non-water content aka dry weight). The ruffage content was 1kg at the beginning. At the end, the ruffage content can’t be 2kg. The 2% ruffage means the total weight is 50kg, so the ruffage stays constant at 1kg.
I absolutely agree with what a few others have commented - there is a massive assumption being made that 'water content' MUST mean 'content by weight', when it could just as easily mean 'content by volume'. This makes the problem unsolvable, because there are then two unknowable variables. To further make the point, imagine what happens if those watermelons are immediately forwarded on by train to another destination and their water content then drops by a further 1% to 97% of the original. According to the given solution, 1% of the original water content weighs 50kg, so if the above extra trip is made, the resulting cargo would be weightless (despite still having a 97% water content AND an 'other' content that the solution assures us weighs 1kg). Another alternative way to highlight the problem's ridiculousness as stated... take the watermelons after their initial journey to an industrial dehydration plant that desiccates them entirely, removing all water content. That would then remove the remaining 98% of water, which according to the problem must weigh (98 x 50kg) in total... or 4,900kg, all-in. By removing 4,900kg from a 50kg weight, you've just invented anti-gravity. Forget rocket fuel... desiccated watermelon is apparently all that you need to escape earth's gravity. Strikes me just perhaps as false (or lazy) assumptive logic...
"That would then (...) 4,900kg, all-in." Why would it weigh that much? If it's 1 kg. solids and 50 kg. in total, the 98 % water must weigh 49 kg. You're off by two orders of magnitude. Your error is apparently in multiplying 50 kg. with 98 (9.800 %) instead of 0,98 (98 %).
@@knrdvmmlbkkn you miss my point. I agree with what you say. However... The presented solution to the problem states that the cargo was originally 1% solids and 99% water, the overall cargo weighing 100kg. The cargo then loses water through dehydration, ending up as 2% solids and 98% water. The claim is that the end weight of the entire cargo is then 50kg. The weight of this minimal water loss is then clearly 50kg, leaving 50kg as the 'end weight', the 'final cargo' being 2% solids and 98% water. Now... send that cargo on another hot journey, so that a further 1% of water evaporates, with the cargo then ending up as 3% solids and 97% water. How much weight is lost over that latest journey?
@@daveyaitch"you miss my point." Apparently I do, and that comment didn't make it any clearer. It mostly just repeats the calculation. Except that I don't see how that water loss could be described as "minimal" (as it's about 50 %).
"According to the given solution, 1% of the original water content weighs 50kg" This is incorrect. According to the solution, in order to change the ratio of solid:water from 1:99 to 2:98, we need to lose 50Kg of the water. Let me put it this way. We start off with 100Kg = 100% of the mass, 99% being water and 1% being solid. If you take away 1kg of water, you will have 98Kg of water and 1Kg of solid and 99Kg now = 100% of the mass. So, now 1Kg = 1.01% of the total mass of 99Kg. Multiply that by 98, the mass of the water content, and we get 98.98% water, _not_ 98% as stipulated by the problem. Whereas, if you think in terms of ratios instead then 1:99 states that 1Kg, 1%, of the mass is solid. A ratio of 2:98 states that 1Kg, _2%,_ of the mass is solid. If 1Kg represent 2% of the new mass then 49Kg represents 98% of the new mass. It's an interesting puzzle and it teaches us that our intuition does not always send us in the right direction. That's the lesson I myself learned from this problem. :D
@@daveyaitch "Now... send that cargo on another hot journey, so that a further 1% of water evaporates, with the cargo then ending up as 3% solids and 97% water. How much weight is lost over that latest journey?" Okay, instead of 97%, consider the weight when the water content falls to _50%._ This would mean that 50% of the weight is solid and 50% is water. The 50% solid part weighs 1Kg and therefore, the total weight would be a mere 2Kg. Make sense?
One way to think of it is that the percentage of dry weight goes from 1% to 2%, so it doubles. Along with the fact that the amount of dry weight remains constant, in order for the percentage to double, the total weight must halve, so the final weight is half of 100 kg, 50 kg. 50 = 100/((1-98%)*(1-99%))
Yes, I think it's interesting that reformulating the question to be "the dry weight percentage increased from 1% to 2%" probably would produce much different results.
Yes, as a fellow ChemE, I was thinking the same thing. This is what we do every day. No decent ChemE should ever get this wrong! We know from experience how much minor changes in %concentration can make such a huge change in lbs total removed. Presh could have plotted an X-Y chart of "Change in total weight" VS "Starting %Water" (1% drop in %Water at each point) and use this to show how this 'change in total weight' heavily depends on the starting %Water.
I came here to say the same. Before becoming a ChemE, I solved problems like this using cross multiplication when I was studying for my technical level degree in Chem.
i remember this one but with potato they lose half of their mass because the 1kg solid content does not change and in order to get 2% solid from 1% you need to halve the water content
It becomes easier to visualize, if instead of saying “99%” and “98%”, you say “99/100ths” and “49/50ths”. Still challenging for many, but that difference in the denominator helps some people.
silly point. 98% is a real percentage used all the time. converting to a fraction and simplifying it is taught in primary school. children learn to do this.
Interesting to me is that removing more than half of the water (50/99) only decreases the water content by 1% units Edit: I meant concentration or ratio instead of content
Looking at it the other way: "NOT water" has DOUBLED from 1% to 2%. This is a huge change. Since "NOT water" it is a constant (1kg both before and after), then water weight must have halved to produce that change.
@@themyief2406yeaisnt the accurate way to say it you reduced the water content by 1 percent. Yea that's right. Because it dropped from 99.percent to 98 oercent water..so it's loterally correct to say the water content dropped by 1 percent..not sure where he got 50/99 from.
@@leif1075 Ok, I had a hard time understanding your comment as it has improper grammer, but I think what you meant by your comment was "It is alright to say that the water content dropped from 99% to 98%". But that would be incomplete, as it should be, "the water content dropped from 99% of starting weight to 98% of final weight". Edit: Also it is incorrect to say that the water content dropped by 1% as the basis of measurement (i-e starting weight and final weight) are not same.
Well, the "dry mass" can't exactly evaporate, so that mass remaining the same is an obvious deduction to make. Not everything should have to be "proven" in problems like this, because then you can start to demand proof of the fact that 50 is indeed half of 100 instead of just assuming that it is.
@@bjorneriksson2404 ' "dry mass" can't exactly evaporate' Dry mass can't evaporate, and taking out 1% from the water weight doesn't make water magically drop to 50 kg from 99 kg. You guys realize at the 4:30 mark where the math is taking the ALREADY REDUCED TOTAL WEIGHT of 99 kg and multiplying it by '98%' which is NOT THE WATER REDUCTION FACTOR to get the 'paradox' is bad math, not a paradox, right? OF COURSE it reduced it too far, that 98% is self references 100%, not 'only the water weight reduction starting at 99%'. This is brain rot, I highly suspect the whole 'bunch of PhD's all arrived at this same answer after being told it was wrong' is completely made up garbage. If it was 100% water weight, and it reduced a percentage to 99% water weight, it would be 99 kg, it would NOT magically jump down to 50 kg from a 1% reduction. This is ONLY THROWN OFF A TINY BIT by 1 kg of the 100 being solid and not reducing by its 1% as well.
I’m glad you included the final, more “visual” solution. It’ll help, for example, in “dinner-table discussions” where I might want to explain this interesting example to folks who aren’t interested in (or who might not follow) “all that algebra stuff”.
You forgot to ask the fundamental question, " What is the definition of water content / moisture content?" In soil mechanics, the definition of moisture content is the mass of the water divided by the mass off the solids. With this definition, you get very different results. This definition results in the mass of the solid to be 50.25 kg and the initial mass of the water to be 49.75 kg. The final mass of the water is 49.25 kg resulting in a final mass of the melon to be 99.50 kg.
@@michaelgleason4791 we arent talking soil mechanics nor did he say moisture content. clearly, using a water:not water ratio will give different answers to a water:total ratio.
What if the watermelons are all still planted in soil on the train, and gain a bit of dry weight on the trip, thus making the water content fall to 98%? Then they would weigh 99/98*100 = 101.02kg approximately at the end.
@@harisimer I think both cases exist. It would be ideal if everyone had a special aptitude for scientific work. But many people just want to have the degree because it helps them with their carreer and so they torture themself through it.
Oh there's an American politician with a PhD who used the slogan 'Jesus, Babies and Guns' - I forget her name - and who believes the earth is flat and that we live in a 'globe conspiracy'. That might just be a reflection on American universities, I don't know...
I didn’t expect that low mass at the end, but I knew you couldn’t just subtract 1kg, so I decided to write it down and solve it carefully and got the correct result
From the thumbnail: 50 kg. Due to the drying out, [99 kg water + 1 kg non-water] changes into [49 kg water + 1 kg non-water] , so the water content changes from 99% to 98% . 10 minutes of explanation? Okay, let's watch.
I worked it out by trying to get the equation to calculate the water weight, so I ended up with (w - d)/w = 99%. Substituted in the dry weight at 1 and solved for 98%. When I got 50, I figured I was wrong and to just watch the video.
I have a hypothesis as to why people have trouble solving this riddle, its because the question doesn't specify 98% of the starting weight or 98% of final weight. At least this is the reason why I got this question wrong.
From an engineering point of view, the dry weight (the meat) has a little effect on the total weight of the sample. It is mostly water, and the meat weight can be ignored. My approximation was half - 50 kg. Close enough.
I knew the answer right away, and not because I saw the same problem on Vsauce2 (The Potato Paradox). That video is about potatoes and this one is about watermelons. These are different types of food altogether.
You assume that in the start the 99% water is 99% of the weight. That is never said in the question. If we do the math by what is said, then in the end the water is again 98% of the watermelons, not the watermelons weight. Then it's a simple ratio problem: Ws = starting weight Wf = final weight Ws = 100kg 99 / Ws = 98 / Wf 99 / 100kg = 98 / Wf 99 * Wf = 98 * 100kg Wf = 98kg / 99 ~ 98.99kg
@@VanjaZavisin 99% and 98% are ratios already by themselves. An equation like 99/Ws=98/Wf would answer a different question, like "We had 100kg of watermelons of which 99kg was water. Then we gave a piece of watermelon to a friend and were left with 98kg of water. What was the total weight of the remaining watermelons?". So here the proportion remains constant. The question posed in the video explicitly states that the proportion of water to watermelon changes.
@@LLlAMnYP I understand what the given solution says, but it is wrong in equating 1% of the watermelons with 1kg of watermelons. That is not said in the problem, hence, water being 99% of the watermelons could be 1kg instead of 99kg. So when the ratio in the end changes, it being 98% would not change the end weight significantly. let alone half it. Just to be clear, it's not "clever wording". The word "content" does not imply weight in any context.
This is a TRICK QUESTION! Everyone assumes that the watermelons lost water weight, but this is NOT stated in the prompt. The train is actually a portable greenhouse with soil and sprinkler system. The water weight of the watermelons stayed at 99 kg while the dry portion of the watermelons grew just over double to ~2.02040816327 kg (equal to 99/49). This increase in dry weight means the watermelons still have 99 kg of water, but this now only constitutes 98% of the total weight. Thanks for coming to my Ted Talk.
Yes!!!! Full agreement. But in practice, I doubt that what is measured is mass. We usually measure weight and erroneously call it mass (or rather label the weight "kg" in error). I've never tried it but I suspect that if you weigh the same pack of, say, flour or sugar or whatever with ordinary scales at the poles or at the equator, the figure will be different but say "kg" when in reality it should be the weight in Newton. But then, the precision of these scales will probably not be good enough to measure that difference. Still, even though this is a math and not a physics puzzle, I think Presh should be more precise and use correct terminology. I'm sure he's aware of the difference.
No. If it was %volume then it would be unsoivable because you'd have to know the density of watermelons. Any reasonable person, or anyone who's ever read almost any food ingredients label, will assume that it means % by weight (and only pedants will point to the distinction between weight and mass).
@@SmileyEmoji42 Did anybody talk about volume here? I don't think anyone did. As for the distinction between weight and mass, it may sound pedantic for ordinary people, but for folks with an affinity to physics (such as me) the difference is not at all trivial. I'm not Don Quixote, I won't be fighting against these windmills because I know it's a lost cause; I've accepted that in colloquial speech weight and mass is often used incorrectly. But in a place where people might not only be interested in math but also science, I think it's totally fine to remind people of the difference. People (and I don't exclude myself) sadly have so many misconceptions that there's no harm, in my opinion, to remind them from time to time of the actual facts. If nobody pointed out these misconceptions, how are any of us supposed to get rid of them?
I hated math, algebra, and calculus. Until you walked through this problem. Wow. I clearly had subpar teachers. Perhaps I would have stayed in the science field. Kudos.
@@baze3541Same my math teacher in highschool was so strict that everyday the test is different from what.we learned which yeh it's just so strict and evil She told us to advance in the book And she gave us a test that wasn't In the book and yeh I call her evil and strict
Yeah, well I loved science and math, but I often see arguments that make something so clear I realize my teachers were not all first class. The super-great teachers are few and far between, but could really improve the learning for students having a hard time. I suppose that is the mark of a good school, where the school recognizes and hires the best teachers.
It baffles how/why someone could think substituting watermelons with potatoes would make sense. What type of potato would have its water content be 99%? Google tells me that raw potatoes contain ~79% water, and cooking them only brings that number down. But because this riddle/paradox is mentioned so many times online, google suggest questions like "Are potatoes 99% water?" and then give the "suggested answer" from a page rephrasing this riddle.
Very surprising. There is a geometric reduction down to just 1kg at 0%. But the greatest weight loss is that first percent. I guess the mistake comes from not noticing that the dry mass % doubled when you went from 99 to 98% water.
Assuming that this was on Earth with standard gravity, the real answer should be 490N, since kg is a measure of mass, not weight. Or alternatively the answer is 110# (avoirdupois), since the pound _is_ a measure of weight.
U could have taken the mass of watermelon to be constant and 1%of 100kg = 2% of end weight of watermelon (as 98% was water and the remains 2% was constant)
I dont think this question is written clearly because i thought that the water would decrease and more of the watermelon would be dry I didn't interpret it that the dry part would stay unchanged
My solution was: 100 = a+b, where a is the water content (99 kg) and b is solid (1 kg) That yields that water percentage is 99/100 = 0.99 At the end of the journey, the water content had dropped to 98%. Let's describe the lost matter as r. The solid is still 1 kg, thus (99 - r)/(100 - r) = 0.98 99 - r = 98 - 0.98r 1 = 0.02 r r = 50 So 50 kg is the lost matter, so water content is 49 kg and total is 50 kg. Let's test it, total weight is thus 50 kg, and 49 kg water out of 50 total is 98%.
This is very strange, the "other" in a watermelon shouldn't increase, I mean I get that since content is 98% and the total should be 100% it means 1kg is 2% now, but you'd assume you lost 1% water and the total is just 99% now idk, doesn't feel logical.
You’d assume that, but since it never said you lost 1% water, that assumption is wrong. If we assume the dry weight stays the same (iffy, but it’s an assumption), then the 99 kg of water drying down to 49 kg would indeed leave you with now 2%*50kg=1kg dry content and 98%*50kg=49kg water. Instead of looking at it from the initial perspective, backtracking it makes it clear that the math from 99 kg of water to 49 kg of water is just a random amount of water loss, and the math that followed is the stipulations in the original problem
3:32 -- mate, *you're **_VERY_** WRONG ...* We are told in the riddle that the ratio of *volume of **_MATTER_* is 99 water to 1 fruit.... *NOT* that the ratio *OF WEIGHT* of water to fruit is 99 to 1... -_- Substances have different densities, you know ?? -_- *REAL ANSWER:* The watermelon has lost 1/99 of its weight during the trip. 1/99 of 100 kg is 1.01 kg. Therefore THE FINAL WEIGHT of the watermelons is ... 100 kg - 1.01 kg = 98.9898(repeat) kg... -_- *PERIOD.* .
But if we don’t assume these ratios are weight, how are you getting an alternate answer? E.g.,, couldn’t the melon portion weigh 40kg, and the water portion weigh 60kg? If that’s the case wouldn’t your alternate answer be wrong?
@@ExtraTrstl I got the same answer they did from the same assumption. My first thought was "That's volume, not mass, right?" and then I decided to play along with "Well, if we assume that the mass is that proportion too..", but since I had already imagined the scenario by volume I found the mass in that scenario instead of the one they were asking for. That's the thing about this paradox, it's not a situation leading to an unexpected result so much as a trick designed to make you misunderstand the situation. And that's also why people complain about it not being a "real" paradox. Any situation can be paradoxical at first glance if you word it poorly enough, and this feels like a more elegant version of that fact, rather than an inherently paradoxical situation.
nope youd get the same answer. it was 1 fruit to 99 water before (total 100) and then it was 2 fruit to 98 water after (total still 100). 2:98 can simplify to 1:49 (divide numerator and denominator by 2) and you get the solution.
@@jonathanodude6660 Imagine you have a spherical watermelon shell that weighs 1 kg. Now imagine it's 99% full of water, and the water weighs 99 kg. Some of that water evaporates, and now it's 98% full of water. What does it weigh? It weighs 98.98kg. That's the most intuitive scenario when you're viewing the water content as a percentage of volume, because any water that evaporates off will be replaced by air. That is also not the situation the problem is actually talking about, which leads to people feeling mislead.
English across world is pronounced and written differently, people will get it wrong even if relative grammar is correct. Comprehensive skills do not work when question is deliberately worded to create confusion and change meaning which could be expressed with more words. Welcome to languages 101.
Question isn't "badly worded", but it is misleadingly worded. And intentionally so. Something is paradoxical if it leads to a counter-intuitive outcome, but in this case it isn't the outcome that's counter-intuitive but the situation itself. The wording leads you to believe that it went from "99 parts water" to "98 parts water". "Water content" can also refer to either mass or volume, which can add another layer of first glance processing to distract from the actual situation. If you give a more clear wording that lends itself to understanding the situation better, like "99% of the original 100kg weight is water" and "98% of the new weight is water" suddenly a lot more people will get it right on the first try.
@@driftwisp2797 99% water content and then 100kg total mass is very unambiguous, obviously its 99% by mass, ie 99kg they never mentioned any volume, so how can you assume it? sounds like excuses to me. if you do not understand what 98% by mass means then maybe you would have trouble. saying "the water content is now 98%" is functionally identical to saying "98% of the new weight is water" because that is what water content means. it is not badly worded nor is it misleading. I am 52 seconds into the video and i have solved it.
The problem most definitely was ambiguously worded. The correct answer is that the final weight of the watermelon batch can not be determined. The problem said "... In the beginning, their water content was 99%. ...". But their water content was 99% of WHAT? Was it 99% of the total weight of the watermelons (which would make their water content 99 kg) or was it 99% of the weight of the watermelons original water content, which was not told to us? It should have said "In the beginning, their water content weight was 99% of the total weight of the watermelons".
@@jameswalsh318 the only explanation for your misunderstanding is that you simply don’t know what “water content” means. That’s not the fault of the question, nor does it make the question poorly worded. If I asked you a puzzle about harmonic oscillation and you thought I was talking about music, that would not mean that the question was poorly worded, because that is the correct name for the phenomenon. The water content of a material is the amount of the material that is water. A water content of 99% means that 99% of the material is water. The question immediately states the material weighs 100kg. The assumption therefore is that 99% corresponds to mass (% w/w), not volume, not density, not refractive index nor anything else. If you’ve ever seen milk say “99% fat free”, it’s not because they removed 99% of the fat present, it’s because 1% of the reduced fat milk is fat and 99% is everything else (water, protein, calcium, etc). That is poorly worded in my opinion. Saying the water content is 99% is correct and the mass immediately provides a disambiguation of the units used to calculate the 99%. If the water content becomes 98%, that means enough water has evaporated to change the total amount of everything and there is a new ratio of water to everything else. This is meaningless information unless we know that the mass of everything else is. Fortunately, there is context behind the question that lets us assume that the mass of everything else never changed. Hence 1kg is now 2%, therefore the total is 50kg.
Hmm, you can think of it this way: If the water content is now 98%, that meams the fraction of the other material is 2% which is double, so the way to make it double is to either double the amount of the other material or halve the amount of water Stage 1 - 1:99 ratio Stage 2 - 2:98 => 1:49 ratio
The puzzle isn't solvable, because content is not the same as mass. That means that 99% of water can theoretically weigh 1 kg while the 1% potato 99kg. A more imaginable example to explain this would be an Iron Mug that is filled with water. The iron mug itself is very heavy. There's more water in the mug than iron. Even if I would empty the whole mug it wouldn't just half it's weight.
@@keith6706 -- Wrong! The person's objection is totally relevant, because the wording is inconsistent/fawlty. You are making excuses, and you are just hijacking the thread.
In the end there is 2% (100% - 98% = 2%) of dry matter. Dry matter should still weigh exactly 1 kg (because it didn't evaporate) given by initial 100 kg * (100% - 99%) = 1 kg The weight where 2% would be exactly 1 kg is 50 kg because 50 kg * 2% = 1 kg (thus 1 / 2% = 50)
This one reminds me of the Monty Hall 3 door problem in that almost everyone gets it wrong at first. The difference is that with the Monty Hall problem, many smart people still won't get it even after the answer is explained.
People get the Monty Hall Problem wrong because the rules the host follows are not made clear: The host must choose one of the two doors you didn’t choose The host must choose a goat, and not a car If you choose a car (probability 1/3), the host can choose either of the other doors, and you shouldn’t change If you choose a goat (probability 2/3), the host must choose the other goat, and you should change Therefore there is a 2/3 probability that changing the door is a good idea. If the host chose another door at random and it happened to be a goat, then the correct answer is different. In that scenario, it makes no difference whether you change.
@@katrinabryce Wait, so the host always chooses the door with the other goat if you've chosen the door with the goat? So the host knows what is behind the door that you've chosen and knows also what is behind each of the other doors and knowingly chooses the door with the other goat? And in the case that you've chosen the door with the car he also knows that it is the door with the car and chooses one of the other doors randomly, knowing there will be a goat behind either door? I hardly remember the problem and my questions are based almost entirely on the comment of your I'm replying here. So there is likely no use in properly explaining the "Three Door Problem" to me. I'd be intersted in a confirmation or correction of the things I've written above.
@@camelopardalis84 Yes, that is correct. And the reason people give the wrong answer is because this isn't made clear in the question, and people assume the host chooses another door at random. Knowing that it isn't a random choice is key to the calculation.
This is why I hate word math problems. If you lose 1% water weight, that will affect the "dry" part of the watermelon. Thus, the dry part wouldn't be the same. Doing this in real life would yield different results.
I have a barrel of water. The barrel itself weighs 1kg, the water in it weighs 99kg. The barrel is open at the top and 1% of the water has evaporated. Are you saying the barrel of water will weigh 50 kilograms?
No. According to your interpretation, the barrel of water would weigh 99.01kg. However, the problem is formulated somewhat differently. It is not stated that 1% of the water evaporated, but rather that the percentage of water in the total volume decreased by 1, which significantly changes the situation. Let me try to explain using your example: Initially, in a barrel weighing 1kg, there were 99kg of water - this means that the ratio of water to the total mass was 99 to 100 or 99%. After 1% of the water evaporated(0.99kg), the ratio of water to the total mass became 98.01 to 99.01, or approximately 98.99%. In order to achieve 98% water content in the total volume for two masses differing by 1 kg (the weight of the barrel), it is necessary to take 49 as the mass of water. In this case, the total mass will be 50, and the ratio will be 49 to 50, which is the solution to the problem.
I approached this by considering the difference in start weight (Xs) and end weight (Xe). Since the weight of melon solid doesn’t change, Xs-Xe=Ws-We, where Ws and We are the weights of water. We know Ws=0.99Xs and We=0.98Xe. Substitute in and rearrange to get 0.01Xs=0.02Xe. So Xe=1/2Xs=50kg.
But did your result answer the question asked? They asked the final weight, so the answer should be either 110 pounds or 490 newtons. kg is a unit of mass.
Leaving aside the fact that the pound is a mass unit, you are oversimplifying matters. Weight including or excluding the buoyancy force due to displaced air? Which definition of weight are you using? The latter could be significant in an accelerated environment such as the surface of the rotating earth. And that's only for starters... 😉😂
I deeply distrust percentages because they have betrayed my intuition a good number of times. So I went through it very rigorously and skeptically and arrived at the correct answer from the beginning. Maybe getting the correct answer or rather, not getting the incorrect answer without noticing, involves a good portion of knowing your limits. I did it in only two simple steps: 1. the initial "dry" percentage is 1% of 100kg so that's 1kg. 2. the end "dry" percentage is 2%, so the total weight is 1kg / 2% = 50kg
the problem doesn't state whether the melon is 99% water by weight or by volume. Water may have a different relative density than the other components of the watermelon.
It's a simplified hypothetical, not an actual physical sitituation. It's implied from the context that 99% refers to kilograms, and that's enough. Asking if it's by weight or by volume is either unnecessary pedantry or inability to understand context. Also, you should have said "mass", not "weight", because those are different things in physics - if you want to be nitpicky, don't leave yourself open for nitpicking.
Think of it as the dry weight doubling from 1 to 2 percent, but remaining at 1kg. So the total weight must be halved resulting in a large amount of water weight being lost. When I first encountered this (with potatoes instead of watermelon) all I could think of is how this must be one long train ride and that the potatoes would rot before losing that much moisture, and that it on a cellular level, losing moisture must be way more complex than it is in this brain teaser. But that it is exactly that, a brain teaser, and the laws of the real world don't apply.
It means "98% water by mass." The total mass is M, and the mass of the water is W, and the mass of the watermelon rind is R. M = W + R, and 0.99M = W, and 0.01M = R.
@@wiggles7976 That formula works but, the interpretation opens a bit after dropping to 98% W = 0.99, R = 0.01 thus M = 1 Okay W/M = 0.99 (99%) Does the formula become W/M(initial) = 0.98 (98%) thus W = 0.98 R = 0.01 M(new) = 0.99 or W/M(new) = 0.98 (98%) thus W = 0.49 R = 0.01 M(new) = 0.5 It depends entirely on the frame of reference.
@@Kitasia if the water content changes, the ratio has changed. the water content of an object in the presence has no dependence on the ratio of that object in the past. W is W(new). W(new)/M(initial) bears no connection to reality. M is always solids + water. changing the water content changes M.
I did it a little differently. If the starting weight is 100kg and the water weight is 99% of that (99kg), the ratio is obviously 99(water)/100(total). If we lose water weight, we lose it from both measures, so (99-x)/(100-x) = 0.98. (99-x)/(100-x) = 0.98 99-x = 0.98(100-x) 99-x = 98-0.98x 1 = 0.02x 100 = 2x 50 = x
But you know the mass of the "dry" portion (or at least can calculate it without problem). It is stated that the total weight at the beginning is 100kg and that the water at the beginning is 99% of total weight. It's a basic elementary school calucation to calculate the non-water mass
@@alam5055 It depends on how you read it, it says that water is 99% of the total content, which I would take as by volume. That last 1% of volume could be like uranium or something.
I solved it by solely considering the dry weight, since it is a fixed value. Both in the beginning and end, we have 1kg of dry weight. However, this same dry weight which accounted for 1% of the initial weight now accounts for 2% of the final weight. If 1kg is 2% of the final weight, then I multiply that by 50 to get 100%, which equals 50kg.
I think the most straightforward way to describe this trick (for me at least) is just looking at the dry weight (I suppose pretty much like your graphical demonstration but kind of in reverse?) The reason I'm calling it a trick, I don't think its a riddle or a puzzle, is because the only thing that's difficult to understand is the phrasing of 99% vs 98% water content. Intuitively we look at that and think "small change". but if you had just phrased the problem in a more straightforward way; something like "if the fraction of dry mass doubles due to loss of water, how much water was lost?" most people's intuition would jump to something pretty close to the correct solution.
I worked it out by saying 1kg of dry weight of the original represents 1% of the total weight. After the journey, that 1kg represents 2% of the total weight (100 - 98). So 1kg = 2/100 x the final weight w. 1kg = 1/50w means total weight is 50 kg
if you think of it in ratios it is very obvious. if you conclude that dry is a constant, it is simple. it goes from 99%, which is 99:1 (99+1=100). Then it goes to 98%, which is 49:1 (49+1=50). This principle is common in gambling. if you are getting a 99% chance of victory, the payout is 99:1 odds. if the chance of victory drops to 98%, the odds go to 98:2, which reduce to 49:1.
I have a problem with you initially stating that "their water content was 99%" and then later at 3:33 you say "water is 99% of its weight". Content and weight (actually mass) are different things entirely. The question is flawed.
It's a math problem, not a physics one, and it's defiinitely not a real life situation. It's basically just asking you to solve an equation, the whole watermelon stuff is just irrelevant fluff. So it's completely normal for it to use colloquial language, instead of precise physical terms, *and* it's pretty damn easily understood from the context that it refers to the weight. It's like asking for specific geographic coordinates of point A and point B from an elementary or middle school math book, to see if there are any turns, road crossings, railroad works, or bridges/bodies of water on the way of the train, to see if something may slow it down, or what th weather conditions are like, etc. It's just a hypothetical train going from a hypithetical point A to hypothetical point B on a hypothetical stretch of a straight line. No need to overthink it this much.
The only plausible interpretations of "content" are percentage by mass, or percentage by volume. Since we aren't given the necessary information (i.e. density) to do volume calculations, it seems prudent to assume that "content" refers to mass. In an exam situation, one could simply state this assumption before answering the question.
@@johncheshirsky8822 -- *No, you're wrong.* The original poster in this thread is correct. Your overly long post with its tangential remarks just made excuses for this fawlty problem. Your post was reported as misinformation. It is best for you not to make posts like this.
@@weevilinabox -- No, in an exam situation, besides this Fawlty problem, it had better use the proper terminology consistently throughout the statement.
Mkay. I think it boils down to "there is always 1 kg of plant" 0.99 = water / (water + plant); solve for water, get 99kg of water and 100 kg total. 0.98 = water / (water + plant), solve for water, get 49kg of water and 50 kg total.
I have solved it quickly with a method very similar to your latest solution. If 1kg dry part was 1% but becomes 2%, then 100% will be 50kg, which results 49kg of water. Q.e.d Talk to any finance guy (I'm an engineer, not a finance guy) about bond coupons and bond prices on secondary markets. Assume the prevailing interest rate is 1%. Someone issues a long term bond, with a $100 face value, and a 1% yield, which means that every year you will get a $1 coupon payment. Next year the inflation goes up, and the market will demand a 2% yield. What will be the price of the bond? Well, the bond will be traded for $50, because this way the $1 payment (the promised coupon) will mean a 2% yield, as demanded by the market. Obviously this will is a simplification (time to maturity, how sound is the issuer, and so on), but it is exactly the same idea.
This is one of the first things we do as chemical engineers. The key is to do the calculations on the amount that does not change - i.e., the 'dry' mass.
I always did this one in my head. Originally the dry melon 1 kg was 1% of the whole; now that same 1 kg is 2% of the whole. So how much do you have to multiply that 2% to get up to 100%? 50. I have a feeling it would've been harder if the number is weren't so easy to keep in your head.
I don't consider myself particularly good at maths, but my mind went straight to: "From the initial condition it is obvious that the non-water weight is 1kg. In the end that 1kg is 2% of the total weight, so the total weight must be 50kg. I guess that is similar to the 'dots' method, but without the dots 🙂
An easier way to visualize this is to look at the DRY WEIGHT. At first, it's 1%. It DOUBLES to 2%. The only way this could happen is if the water weight was cut in half. So 100kg at 1% becomes 50kg at 2%. What a fantastic puzzle!!!
This sounds more like someone trying to come up with an excuse for why they ate half the melons on the train.
But only the water!
lmao
True
Very good
You can't just assume that 99% of the watermelon's "content" is the same as 99% of its weight.
I don't know why they keep making their questions' wording difficult to understand.
Exactly right!
I think that's the point though, to have the solver make the logical deduction about what the percentage means.
This was my objection as well. We were never given the weight of the water only some off handed remark about the content being 99% water.
it doesn't say 'watermelon content' - it says 'water content,' which is a phrase we use to express the mass of water as a percentage of an object or substances _total weight._ the question explicitly tells you that 99% of the total 100kg is water.
❌i've done half my tasks
✅my performance went from 99% to 98%
not the same statement, though.
Not quite. Like this:
❌ Boss, I sleep only 98% of the time on the job now, instead of 99%!
✅ Boss, I doubled the amount of work I complete every day, I need a pay raise! 💸
@@HxTurtle yeah, more like "I'm doing less than half the work but only lost 1% of performance, yikes!" followed by "but why do you let me go with such good stats? Lost trust? How am I not dependable enough to not assign those tasks?"
@@kubastachu9860 eh a clearer explanation is assuming that the workload halved from 100 tasks to 50, and they went from doing 99 / 100 tasks to doing 49 / 50 tasks. their total task count has to change for this to make any sense.
That's not an equal comparison. In your scenario, your performance went from 0% to 50%, increasing by 10% each time.
If you calculated it based on each task's percentage of the total remaining, it would steadily increase.
For example; completing 1 task out of 10 is 10%, but completing 1 task out of 9 would be 11.111%, etc. When you reached 2 tasks remaining, completing one of them could be stated as completing 50% of the remaining tasks, but you'd still have only increased by 10% for each completed task when compared to the original list of 10.
The false assumption is that there is a 1% loss of water versus the original weight, when in fact it is only a ratio. Using that it becomes easier to understand that youre trying then to work out what weight fits the new ratio rather than thinking of it as having lost 1% of water
Yup, once understanding this, the problem becomes much more simple and obvious. Took me some time though because it's worded(quite well) to lead you to believe the % is not a ratio but rather an ammount
I knew it felt like I was missing something when it first thought about it.
Which is why I was sure you would have to solve algebraically to get it but it's such an easy assumption and mistakes to make if you just read it
Somebody is cheating here with the wording!
I could have sworn the video said 99% of the total weight (100kg) was water.... Or is that what the listener just infers themselves, hence the riddle?
It just sounds like the person removed 1.01% of the total weight...
It's not a "false assumption". It's an incorrectly specified problem.
And that's the real answer: "As specified, this question is too ambiguous to solve".
"dropped to 98%" means what? Is there an actual 1kg watermelon anywhere in the world such that, upon extracting 1% of its water content, its weight magically drops to 50% of its original weight?
The way I see it basically what you did in the end. If 1 Kg of watermelon is now 2% of the weight, the total weight is 50 times 1 Kg.
I solved this myself. I am both confused how much weight was lost but also it kinda made sense
Your method is far more intuitive to me than the ones Presh started with. First notice that 1%, hence 1 kg, is not water. For 98% water, we ask: “1 kg is 2% of what?” This question gives the intuitive answer 50 kg, or can be translated into the equation
1 = .02x, and hence x = 50 kg.
@@theglobalwarming6081 'I am both confused how much weight was lost '
Realize, there's an easier way to see the reduction in weight, take it further.
1kg solid and 99kg water gets the 99% water content.
But to get to 50% water content, you have to have the starting 1kg solid, and only 1kg water left. You have to lose 98kg of the initial 99kg to get down to 50% water content.
The water content percentage being referenced to the 1kg solids instead of an independent reference means the scale slides, and by using 1%/99% to start, the scale slides very hard.
99 kg of water is 26.12137 gallons. Take five 5 gallon buckets of water and another gallon, put them together, and try to wrap it all and hold it together with only 1kg of watermelon skin and rind.
It's a not real problem, specifically chosen to use the self referencing 'water content' with an unrealistically high water content to generate the huge swing in values. It could work in some less familiar things, but you would be hard pressed to do this with a watermelon. Real watermelons tend to be 4% or so solid, they'll be mush before you get to 1%.
That's pretty much what I did.
The water is the thing that changes and it's the unknown. But the mass of everything else is the same before and after.
You start with 100kg total, 99% of which is water. So everything else is 1kg.
The amount after, is still 1kg. You are told that the water content drops to 98%. So that means the percent of everything else is 2%
Knowing that the amount of everything but the water is 1kg, and that the percentage of it is 2% , you can then calculate the total mass of everything as 1kg/0.02 = 50kg
@@ModelLightsfrom what I'm reading, watermelons are 92% water. Perhaps if you remove the inedible green rind then the editable red stuff is 96% water...
my mind went: melon went from 1% -> 2%, doubeling, so weight must be half. then i started think, what did i miss..
You are just genetically superior
didn't make sense to me 'till I read this comment
you got lucky
You missed nowt, that makes perfect sense.
You focused on what WASN'T water, yet the water is the focus of the question (all the information is in terms of it).
People think "oh 99% to 98% isn't much loss", and that's where they get tripped up.
I'm a maths teacher, and I think the problem here is in the application. There has been a movement ( a good one in theory ) to teach maths in context as much as possible, as this makes it more engaging, easier to understand and more valuable. Hence a question about watermelons instead of just algebraic questions.
But if you're going to write a contextualised question, you are signalling to the reader/solver that it makes sense in the real world. So they will expect the answer to be somewhere within the realms of predictability. If one were to guess, no maths involved, how much the watermelons would reduce, one might expect an answer in the realm of a few kilos, so their expectation would confirm the mathematically wrong answer. The mathematically correct answer here is absurd in real world terms. So, don't bother contextualising the question in the real world if it doesn't actually make any sense in the real world.
This goes for any question like, "Little Johnny is trying to find the ratio of white flowers to yellow flowers in the meadow by his house" or whatever ridiculous scenario. There has never been a little johnny who wanted to work that out. This is not a real world example. Has never happened. Will never happen. Try harder or don't bother!
Johnny has autism. Let him count the ratio of flowers.
I take it you've never weighed mushrooms before and after drying them?
You are so right @karyosentiko!
You are a person after my own heart.
I quite agree with your point, but this is a nice problem nonetheless. Perhaps there is a more realistic way of asking it.
Your math solution is correct, but that freight shipping cost will be wasted because the load of watermelons are useless now
Watermelons that are twice as sweet? gimme gimme gimme
Not at all. You can still make watermelon skin jam from it, and the concentrated watermelon juice can be drinkable.
If it is not some kind of maidenless pit free melon, you can plant the seeds next year.
Unless it also rotted. That would leave you with making some watermelon wine or vinegar at best.
They are not useless.
Bowling balls.
The watermelons will not be dry. They are still 98% water. And they will be twice as sweet and flavorful.
This problem is solvable only if you assume that when you say something is 99% water, you mean 99% by weight. However, that is a false assumption. Most people, when they are told something is 99% water, they take that to mean that the volume of the said object is 99% water. Thus you have here two unknowns, you don't know how much the water weighs, and neither do you know the weight of the vegetable component of the watermelon. Therefore, this problem is unsolvable.
Thank you, this is exactly why I concluded the problem is unsolvable. The stated solution makes a big jump from "the water content is 99%" means that "the water weighs 99 kg".
That's what I thought also
It’s” heavy water” the weight is 99kg 😂
It is safe to assume 1 liter of water weighs 1 kg more or less, depending on you location on earth, the temperature and how pure it is and such but that really feels out of scope of this riddle.. :)
Well, I think it's reasonable to assume that 1 litre of water weighs 1 kg.
From 6:26 to 7:07, there is the expression "d=0.1(100)=1" but it should be "d=0.01(100)=1"
They are students at a barbecue. I can think of several reasons why they got the answer wrong, ranging from 4.5% to 40% in volume 😂
😂😂😂 Some even 65%.
😂😂
This was actually hilarious
I can thing of some other reasons. More... plant based, let's say.
This doesn't make sense to me, 1ltr of water is 1kg, so 99% of 100kg is 99kg which is equal to 99ltr. So 98% of 99 is 97.02, the 1kg dry weight doesnt change so the answer should be 98.02kg. I know I must be wrong but I just dont understand why.
If the non-water content goes from 1 (1% of the original mass) to 2% of the new mass it means that we lost half of the original mass. If 1 kg now is 2% the new mass is 50 kg.
This is a much clearer way of framing it.
@@aidanhammer6968 The explanation in the video seems to me unnecessarily complicated.
Wow. Nice!
I wrote out three very simple equations with three variables and did the algebra
Looks like the video basically did what I did. U making me feel foolish
This helped, thank you!
The way I'd explain it is that while a drop from 99% to 98% might seem minuscule, the relative dry weight has doubled from 1/100 to 2/100, or 1/50. And as the dry weight hasn't changed, then it can only mean the total weight has halved.
if you're going to discuss these puzzles as more than "bar tricks", you really should eliminate errors like
1) MASS is not WEIGHT
2) % of total is given in terms of MASS or VOLUME
Calling veridical paradox a paradox itself feels like a veridical paradox.
In the Netherlands this problem was presented about 20 years ago on a national IQ test TV show as a stallholder selling 200kg of cucumbers on a hot day. I remember being stunned by the answer as it is so counter intuitive.
damn,but it's headscratching how flabby dried out potatoes can still consist of 98% water...That's something surreal...
To be honest, a "potato" containing 99% or even "only" 98% of water wouldn't be much of a potato. Even watermelons, according to Auntie Google, don't consist of 99% water.
The figures I found on the quick was 92% water in a watermelon, and 80% in a potato.
... And adult human male is 60% water
@@beepbop6697 Well yeah, both give a big wet splat when you chuck them out of a 12th story window.
simple explanation: assuming the non-water part of the melons didnt change, that part is still 1kg. that 1kg is now 2% of the total mass, or 1/50th, meaning the rest is 49/50ths, or 49kgs.
I think one reason for the confusion by many people is because they (like I did initially) interpret the "water content" as a percentage of the VOLUME instead of the WEIGHT. I pictured watermelon-shaped containers 99% full of water changing to 98% full of water, which is a different problem. :P
What changes if it's volume? Just like weight, the overall volume would reduce as well.
@@LLlAMnYP Bro, What if it was 98% water, 1% Dry stuff, 1% Vacuum? Consider the watermelon is a closed system.
@@lifeisajourney4340
> watermelon is a closed system
Awww, hell no it ain't! XD
@@LLlAMnYP What about the other question?
@@LLlAMnYP if it's just a single percent drop in volume, there is no guarantee it would equate to 50kg, or 40kg or 37kg, or anything, because we don't know what the volume to weight ratio is.
This was my problem too, and couldn't seem to solve the equation this way.
To be fair, the question does not mention that the dry weight remains the same during the journey, so we can come up with any numbers for the answer, as long as the water content is 98%.
You have the calculation of "final dry weight" misrepresented at 6:34. It shows "d = 0.1(100)", when it should show "d = 0.01(100)". (FYI)
For me the visual part makes sense if the dry weight was 2 yellow dots with 98 blue then " simplify" to 1 yellow and 49 blue.
The better way to think about it to use units that are invariable rather than units that are variable. Water content is variable, so let’s rephrase it into ruffage content (non-water content aka dry weight). The ruffage content was 1kg at the beginning. At the end, the ruffage content can’t be 2kg. The 2% ruffage means the total weight is 50kg, so the ruffage stays constant at 1kg.
Skip to 4:57 for mathematics. The previous part is unnecessary social media speculation.
I absolutely agree with what a few others have commented - there is a massive assumption being made that 'water content' MUST mean 'content by weight', when it could just as easily mean 'content by volume'. This makes the problem unsolvable, because there are then two unknowable variables.
To further make the point, imagine what happens if those watermelons are immediately forwarded on by train to another destination and their water content then drops by a further 1% to 97% of the original. According to the given solution, 1% of the original water content weighs 50kg, so if the above extra trip is made, the resulting cargo would be weightless (despite still having a 97% water content AND an 'other' content that the solution assures us weighs 1kg).
Another alternative way to highlight the problem's ridiculousness as stated... take the watermelons after their initial journey to an industrial dehydration plant that desiccates them entirely, removing all water content. That would then remove the remaining 98% of water, which according to the problem must weigh (98 x 50kg) in total... or 4,900kg, all-in. By removing 4,900kg from a 50kg weight, you've just invented anti-gravity. Forget rocket fuel... desiccated watermelon is apparently all that you need to escape earth's gravity.
Strikes me just perhaps as false (or lazy) assumptive logic...
"That would then (...) 4,900kg, all-in."
Why would it weigh that much? If it's 1 kg. solids and 50 kg. in total, the 98 % water must weigh 49 kg. You're off by two orders of magnitude.
Your error is apparently in multiplying 50 kg. with 98 (9.800 %) instead of 0,98 (98 %).
@@knrdvmmlbkkn you miss my point. I agree with what you say. However...
The presented solution to the problem states that the cargo was originally 1% solids and 99% water, the overall cargo weighing 100kg. The cargo then loses water through dehydration, ending up as 2% solids and 98% water. The claim is that the end weight of the entire cargo is then 50kg.
The weight of this minimal water loss is then clearly 50kg, leaving 50kg as the 'end weight', the 'final cargo' being 2% solids and 98% water.
Now... send that cargo on another hot journey, so that a further 1% of water evaporates, with the cargo then ending up as 3% solids and 97% water. How much weight is lost over that latest journey?
@@daveyaitch"you miss my point."
Apparently I do, and that comment didn't make it any clearer. It mostly just repeats the calculation. Except that I don't see how that water loss could be described as "minimal" (as it's about 50 %).
"According to the given solution, 1% of the original water content weighs 50kg"
This is incorrect. According to the solution, in order to change the ratio of solid:water from 1:99 to 2:98, we need to lose 50Kg of the water.
Let me put it this way. We start off with 100Kg = 100% of the mass, 99% being water and 1% being solid. If you take away 1kg of water, you will have 98Kg of water and 1Kg of solid and 99Kg now = 100% of the mass. So, now 1Kg = 1.01% of the total mass of 99Kg. Multiply that by 98, the mass of the water content, and we get 98.98% water, _not_ 98% as stipulated by the problem.
Whereas, if you think in terms of ratios instead then 1:99 states that 1Kg, 1%, of the mass is solid. A ratio of 2:98 states that 1Kg, _2%,_ of the mass is solid. If 1Kg represent 2% of the new mass then 49Kg represents 98% of the new mass.
It's an interesting puzzle and it teaches us that our intuition does not always send us in the right direction. That's the lesson I myself learned from this problem. :D
@@daveyaitch "Now... send that cargo on another hot journey, so that a further 1% of water evaporates, with the cargo then ending up as 3% solids and 97% water. How much weight is lost over that latest journey?"
Okay, instead of 97%, consider the weight when the water content falls to _50%._ This would mean that 50% of the weight is solid and 50% is water. The 50% solid part weighs 1Kg and therefore, the total weight would be a mere 2Kg.
Make sense?
One way to think of it is that the percentage of dry weight goes from 1% to 2%, so it doubles. Along with the fact that the amount of dry weight remains constant, in order for the percentage to double, the total weight must halve, so the final weight is half of 100 kg, 50 kg.
50 = 100/((1-98%)*(1-99%))
That makes so much sense, thanks!
Yes, I think it's interesting that reformulating the question to be "the dry weight percentage increased from 1% to 2%" probably would produce much different results.
Chemical Engineers: Material Balance....
Yes, as a fellow ChemE, I was thinking the same thing. This is what we do every day. No decent ChemE should ever get this wrong! We know from experience how much minor changes in %concentration can make such a huge change in lbs total removed.
Presh could have plotted an X-Y chart of "Change in total weight" VS "Starting %Water" (1% drop in %Water at each point) and use this to show how this 'change in total weight' heavily depends on the starting %Water.
I came here to say the same. Before becoming a ChemE, I solved problems like this using cross multiplication when I was studying for my technical level degree in Chem.
But how old is the driver?
And how freshly does his toad walk?
Because he has neither a fish.
The driver is 98, but real thirsty!
But how old are the watermelons?
But how many watermelons were there?
i remember this one but with potato
they lose half of their mass because the 1kg solid content does not change and in order to get 2% solid from 1% you need to halve the water content
It becomes easier to visualize, if instead of saying “99%” and “98%”, you say “99/100ths” and “49/50ths”. Still challenging for many, but that difference in the denominator helps some people.
silly point. 98% is a real percentage used all the time. converting to a fraction and simplifying it is taught in primary school. children learn to do this.
@@jonathanodude6660be gone hater
@@SeanSFM no.
Interesting to me is that removing more than half of the water (50/99) only decreases the water content by 1% units
Edit:
I meant concentration or ratio instead of content
Looking at it the other way: "NOT water" has DOUBLED from 1% to 2%. This is a huge change. Since "NOT water" it is a constant (1kg both before and after), then water weight must have halved to produce that change.
you are wrong here, the 99% was in terms of the starting weight but the 98% was in terms of the final weight.
@@themyief2406yeaisnt the accurate way to say it you reduced the water content by 1 percent. Yea that's right. Because it dropped from 99.percent to 98 oercent water..so it's loterally correct to say the water content dropped by 1 percent..not sure where he got 50/99 from.
Thank you for your coment, now I understand……..I think😅
@@leif1075 Ok, I had a hard time understanding your comment as it has improper grammer, but I think what you meant by your comment was "It is alright to say that the water content dropped from 99% to 98%". But that would be incomplete, as it should be, "the water content dropped from 99% of starting weight to 98% of final weight".
Edit: Also it is incorrect to say that the water content dropped by 1% as the basis of measurement (i-e starting weight and final weight) are not same.
Imagine losing 50kg of water to summer heat. Those melons must be shrivelled messes
Good thing the water content didn’t drop 20 or 30%, the watermelons would be floating off like helium balloons 😂
0:10 I think an attempt was made to do the 'in the beninging' meme and then decide halfway to follow a civilized scientific discourse.
I thought there was some trick involved and was pretty disappointed, when the solution turned out to be just the straight foreward approach.
I got this right, but at 3:58 it is an assumption that the solid mass remained as this was never made clear in the question.
@@JLvatron You are right. It is only implied.
You are right. It was only implued, which is indeed not clear enough.
Well, the "dry mass" can't exactly evaporate, so that mass remaining the same is an obvious deduction to make. Not everything should have to be "proven" in problems like this, because then you can start to demand proof of the fact that 50 is indeed half of 100 instead of just assuming that it is.
Correct, and I have made the same observation, and it seems that, in addition to water, melons contain over 100 different volatile compounds.
@@bjorneriksson2404 ' "dry mass" can't exactly evaporate'
Dry mass can't evaporate, and taking out 1% from the water weight doesn't make water magically drop to 50 kg from 99 kg.
You guys realize at the 4:30 mark where the math is taking the ALREADY REDUCED TOTAL WEIGHT of 99 kg and multiplying it by '98%' which is NOT THE WATER REDUCTION FACTOR to get the 'paradox' is bad math, not a paradox, right?
OF COURSE it reduced it too far, that 98% is self references 100%, not 'only the water weight reduction starting at 99%'.
This is brain rot, I highly suspect the whole 'bunch of PhD's all arrived at this same answer after being told it was wrong' is completely made up garbage.
If it was 100% water weight, and it reduced a percentage to 99% water weight, it would be 99 kg, it would NOT magically jump down to 50 kg from a 1% reduction. This is ONLY THROWN OFF A TINY BIT by 1 kg of the 100 being solid and not reducing by its 1% as well.
I’m glad you included the final, more “visual” solution.
It’ll help, for example, in “dinner-table discussions” where I might want to explain this interesting example to folks who aren’t interested in (or who might not follow) “all that algebra stuff”.
You forgot to ask the fundamental question, " What is the definition of water content / moisture content?" In soil mechanics, the definition of moisture content is the mass of the water divided by the mass off the solids. With this definition, you get very different results. This definition results in the mass of the solid to be 50.25 kg and the initial mass of the water to be 49.75 kg. The final mass of the water is 49.25 kg resulting in a final mass of the melon to be 99.50 kg.
Nonsense. You have inented an ambiguity that does not exist.
Just because you can't say the ambiguity does not make it nonsense. That's a pretty narrow view of the world.
@@michaelgleason4791 we arent talking soil mechanics nor did he say moisture content. clearly, using a water:not water ratio will give different answers to a water:total ratio.
I am a nurse and this is exactly how my mind worked too
Man it makes you feel good when you get these right
You overcomplicate the answer. I just did the dry weight is 1kg, which has to be 2%. So 1kg*50=50kg.
You overcomplicate the answer. I used a scale
What if the watermelons are all still planted in soil on the train, and gain a bit of dry weight on the trip, thus making the water content fall to 98%? Then they would weigh 99/98*100 = 101.02kg approximately at the end.
A PhD doesn't mean you are smart it means you are determined and willing to be hazed with trauma.
No, a PhD shows a special aptitude for scientific work and research. If you are smart that very well might make a difference
@@harisimer I think both cases exist. It would be ideal if everyone had a special aptitude for scientific work. But many people just want to have the degree because it helps them with their carreer and so they torture themself through it.
Oh there's an American politician with a PhD who used the slogan 'Jesus, Babies and Guns' - I forget her name - and who believes the earth is flat and that we live in a 'globe conspiracy'. That might just be a reflection on American universities, I don't know...
I didn’t expect that low mass at the end, but I knew you couldn’t just subtract 1kg, so I decided to write it down and solve it carefully and got the correct result
From the thumbnail: 50 kg.
Due to the drying out, [99 kg water + 1 kg non-water] changes into [49 kg water + 1 kg non-water] , so the water content changes from 99% to 98% .
10 minutes of explanation? Okay, let's watch.
I worked it out by trying to get the equation to calculate the water weight, so I ended up with (w - d)/w = 99%. Substituted in the dry weight at 1 and solved for 98%. When I got 50, I figured I was wrong and to just watch the video.
I have a hypothesis as to why people have trouble solving this riddle, its because the question doesn't specify 98% of the starting weight or 98% of final weight. At least this is the reason why I got this question wrong.
True... The question should have also avoided mentioning that water content DROPPED.. which makes people think it is 98% of initial weight
From an engineering point of view, the dry weight (the meat) has a little effect on the total weight of the sample. It is mostly water, and the meat weight can be ignored. My approximation was half - 50 kg. Close enough.
I knew the answer right away, and not because I saw the same problem on Vsauce2 (The Potato Paradox). That video is about potatoes and this one is about watermelons. These are different types of food altogether.
Lol
Sorry, I only know how to solve this for oranges.
True, you can just plant the potatoes and hope for better luck next year. The watermelon in the picture are seedless, so no such luck.
You assume that in the start the 99% water is 99% of the weight. That is never said in the question.
If we do the math by what is said, then in the end the water is again 98% of the watermelons, not the watermelons weight.
Then it's a simple ratio problem:
Ws = starting weight
Wf = final weight
Ws = 100kg
99 / Ws = 98 / Wf
99 / 100kg = 98 / Wf
99 * Wf = 98 * 100kg
Wf = 98kg / 99 ~ 98.99kg
yeah I got 100 * (98/99) = 98.989898 recurring. this problem was frustrating till I realized it didn't give you all the info.
99/Ws does not equal 98/Wf. Why should it?
@@LLlAMnYP It's a proportion equation. If you know 99% is proportionate to 100kg, and you want to know what 98% is proportionate to. In this case Wf.
@@VanjaZavisin 99% and 98% are ratios already by themselves. An equation like 99/Ws=98/Wf would answer a different question, like "We had 100kg of watermelons of which 99kg was water. Then we gave a piece of watermelon to a friend and were left with 98kg of water. What was the total weight of the remaining watermelons?". So here the proportion remains constant. The question posed in the video explicitly states that the proportion of water to watermelon changes.
@@LLlAMnYP I understand what the given solution says, but it is wrong in equating 1% of the watermelons with 1kg of watermelons. That is not said in the problem, hence, water being 99% of the watermelons could be 1kg instead of 99kg. So when the ratio in the end changes, it being 98% would not change the end weight significantly. let alone half it.
Just to be clear, it's not "clever wording". The word "content" does not imply weight in any context.
This is a TRICK QUESTION! Everyone assumes that the watermelons lost water weight, but this is NOT stated in the prompt. The train is actually a portable greenhouse with soil and sprinkler system. The water weight of the watermelons stayed at 99 kg while the dry portion of the watermelons grew just over double to ~2.02040816327 kg (equal to 99/49). This increase in dry weight means the watermelons still have 99 kg of water, but this now only constitutes 98% of the total weight. Thanks for coming to my Ted Talk.
Question phrasing should say water content was 99% *** of its mass ***
No, it should state "of its mass."
@@robertveith6383yeah your right . I’ll edit the comment
Yes!!!! Full agreement.
But in practice, I doubt that what is measured is mass. We usually measure weight and erroneously call it mass (or rather label the weight "kg" in error). I've never tried it but I suspect that if you weigh the same pack of, say, flour or sugar or whatever with ordinary scales at the poles or at the equator, the figure will be different but say "kg" when in reality it should be the weight in Newton. But then, the precision of these scales will probably not be good enough to measure that difference.
Still, even though this is a math and not a physics puzzle, I think Presh should be more precise and use correct terminology. I'm sure he's aware of the difference.
No. If it was %volume then it would be unsoivable because you'd have to know the density of watermelons. Any reasonable person, or anyone who's ever read almost any food ingredients label, will assume that it means % by weight (and only pedants will point to the distinction between weight and mass).
@@SmileyEmoji42 Did anybody talk about volume here? I don't think anyone did.
As for the distinction between weight and mass, it may sound pedantic for ordinary people, but for folks with an affinity to physics (such as me) the difference is not at all trivial.
I'm not Don Quixote, I won't be fighting against these windmills because I know it's a lost cause; I've accepted that in colloquial speech weight and mass is often used incorrectly. But in a place where people might not only be interested in math but also science, I think it's totally fine to remind people of the difference.
People (and I don't exclude myself) sadly have so many misconceptions that there's no harm, in my opinion, to remind them from time to time of the actual facts. If nobody pointed out these misconceptions, how are any of us supposed to get rid of them?
The thought that illustrated to me just how much weight it would lose is realizing that 50% water content would weigh only 2kg.
I hated math, algebra, and calculus. Until you walked through this problem. Wow. I clearly had subpar teachers. Perhaps I would have stayed in the science field. Kudos.
I had the worst math teacher in high school and yet that did not hold me back from math or anything
@@baze3541Same my math teacher in highschool was so strict that everyday the test is different from what.we learned which yeh it's just so strict and evil
She told us to advance in the book
And she gave us a test that wasn't In the book and yeh I call her evil and strict
Yeah, well I loved science and math, but I often see arguments that make something so clear I realize my teachers were not all first class. The super-great teachers are few and far between, but could really improve the learning for students having a hard time. I suppose that is the mark of a good school, where the school recognizes and hires the best teachers.
It baffles how/why someone could think substituting watermelons with potatoes would make sense. What type of potato would have its water content be 99%? Google tells me that raw potatoes contain ~79% water, and cooking them only brings that number down. But because this riddle/paradox is mentioned so many times online, google suggest questions like "Are potatoes 99% water?" and then give the "suggested answer" from a page rephrasing this riddle.
Very surprising. There is a geometric reduction down to just 1kg at 0%. But the greatest weight loss is that first percent.
I guess the mistake comes from not noticing that the dry mass % doubled when you went from 99 to 98% water.
Assuming that this was on Earth with standard gravity, the real answer should be 490N, since kg is a measure of mass, not weight. Or alternatively the answer is 110# (avoirdupois), since the pound _is_ a measure of weight.
U could have taken the mass of watermelon to be constant and 1%of 100kg = 2% of end weight of watermelon (as 98% was water and the remains 2% was constant)
* *You*
@@robertveith6383 U*
I dont think this question is written clearly because i thought that the water would decrease and more of the watermelon would be dry I didn't interpret it that the dry part would stay unchanged
None of it is dry
How would dried water turn into more watermelon...? That doesn't make any sense.
My solution was:
100 = a+b, where a is the water content (99 kg) and b is solid (1 kg)
That yields that water percentage is 99/100 = 0.99
At the end of the journey, the water content had dropped to 98%.
Let's describe the lost matter as r.
The solid is still 1 kg, thus
(99 - r)/(100 - r) = 0.98
99 - r = 98 - 0.98r
1 = 0.02 r
r = 50
So 50 kg is the lost matter, so water content is 49 kg and total is 50 kg.
Let's test it, total weight is thus 50 kg, and 49 kg water out of 50 total is 98%.
This is very strange, the "other" in a watermelon shouldn't increase, I mean I get that since content is 98% and the total should be 100% it means 1kg is 2% now, but you'd assume you lost 1% water and the total is just 99% now idk, doesn't feel logical.
You’d assume that, but since it never said you lost 1% water, that assumption is wrong.
If we assume the dry weight stays the same (iffy, but it’s an assumption), then the 99 kg of water drying down to 49 kg would indeed leave you with now 2%*50kg=1kg dry content and 98%*50kg=49kg water. Instead of looking at it from the initial perspective, backtracking it makes it clear that the math from 99 kg of water to 49 kg of water is just a random amount of water loss, and the math that followed is the stipulations in the original problem
How many people would have to refrain from voting for your vote to double its' net value? Basically half the total amount of people voting.
I tend to be more of a visual learner when it comes to these kinds of puzzles, so the visual method at 9:15 made a lot of sense to me.
3:32 -- mate, *you're **_VERY_** WRONG ...*
We are told in the riddle that the ratio of *volume of **_MATTER_* is 99 water to 1 fruit.... *NOT* that the ratio *OF WEIGHT* of water to fruit is 99 to 1... -_-
Substances have different densities, you know ?? -_-
*REAL ANSWER:*
The watermelon has lost 1/99 of its weight during the trip. 1/99 of 100 kg is 1.01 kg. Therefore THE FINAL WEIGHT of the watermelons is ... 100 kg - 1.01 kg = 98.9898(repeat) kg... -_-
*PERIOD.*
.
But if we don’t assume these ratios are weight, how are you getting an alternate answer?
E.g.,, couldn’t the melon portion weigh 40kg, and the water portion weigh 60kg? If that’s the case wouldn’t your alternate answer be wrong?
@@ExtraTrstl I got the same answer they did from the same assumption. My first thought was "That's volume, not mass, right?" and then I decided to play along with "Well, if we assume that the mass is that proportion too..", but since I had already imagined the scenario by volume I found the mass in that scenario instead of the one they were asking for.
That's the thing about this paradox, it's not a situation leading to an unexpected result so much as a trick designed to make you misunderstand the situation. And that's also why people complain about it not being a "real" paradox. Any situation can be paradoxical at first glance if you word it poorly enough, and this feels like a more elegant version of that fact, rather than an inherently paradoxical situation.
nope youd get the same answer. it was 1 fruit to 99 water before (total 100) and then it was 2 fruit to 98 water after (total still 100). 2:98 can simplify to 1:49 (divide numerator and denominator by 2) and you get the solution.
@@jonathanodude6660 Imagine you have a spherical watermelon shell that weighs 1 kg. Now imagine it's 99% full of water, and the water weighs 99 kg. Some of that water evaporates, and now it's 98% full of water. What does it weigh? It weighs 98.98kg.
That's the most intuitive scenario when you're viewing the water content as a percentage of volume, because any water that evaporates off will be replaced by air.
That is also not the situation the problem is actually talking about, which leads to people feeling mislead.
@@driftwisp2797 ok but now we are talking about volume measurements which were not given in the question.
When you first started explaining the answer, I was so irked, because I was sure that was wrong.
So many comments suggesting question is badly worded.
To me it sounds like they are trying to invent an excuse for their failed answer.
English across world is pronounced and written differently, people will get it wrong even if relative grammar is correct. Comprehensive skills do not work when question is deliberately worded to create confusion and change meaning which could be expressed with more words. Welcome to languages 101.
Question isn't "badly worded", but it is misleadingly worded. And intentionally so. Something is paradoxical if it leads to a counter-intuitive outcome, but in this case it isn't the outcome that's counter-intuitive but the situation itself. The wording leads you to believe that it went from "99 parts water" to "98 parts water". "Water content" can also refer to either mass or volume, which can add another layer of first glance processing to distract from the actual situation.
If you give a more clear wording that lends itself to understanding the situation better, like "99% of the original 100kg weight is water" and "98% of the new weight is water" suddenly a lot more people will get it right on the first try.
@@driftwisp2797 99% water content and then 100kg total mass is very unambiguous, obviously its 99% by mass, ie 99kg they never mentioned any volume, so how can you assume it? sounds like excuses to me. if you do not understand what 98% by mass means then maybe you would have trouble. saying "the water content is now 98%" is functionally identical to saying "98% of the new weight is water" because that is what water content means. it is not badly worded nor is it misleading. I am 52 seconds into the video and i have solved it.
The problem most definitely was ambiguously worded.
The correct answer is that the final weight of the watermelon batch can not be determined. The problem said "... In the beginning, their water content was 99%. ...". But their water content was 99% of WHAT? Was it 99% of the total weight of the watermelons (which would make their water content 99 kg) or was it 99% of the weight of the watermelons original water content, which was not told to us?
It should have said "In the beginning, their water content weight was 99% of the total weight of the watermelons".
@@jameswalsh318 the only explanation for your misunderstanding is that you simply don’t know what “water content” means. That’s not the fault of the question, nor does it make the question poorly worded. If I asked you a puzzle about harmonic oscillation and you thought I was talking about music, that would not mean that the question was poorly worded, because that is the correct name for the phenomenon. The water content of a material is the amount of the material that is water. A water content of 99% means that 99% of the material is water. The question immediately states the material weighs 100kg. The assumption therefore is that 99% corresponds to mass (% w/w), not volume, not density, not refractive index nor anything else.
If you’ve ever seen milk say “99% fat free”, it’s not because they removed 99% of the fat present, it’s because 1% of the reduced fat milk is fat and 99% is everything else (water, protein, calcium, etc). That is poorly worded in my opinion. Saying the water content is 99% is correct and the mass immediately provides a disambiguation of the units used to calculate the 99%.
If the water content becomes 98%, that means enough water has evaporated to change the total amount of everything and there is a new ratio of water to everything else. This is meaningless information unless we know that the mass of everything else is. Fortunately, there is context behind the question that lets us assume that the mass of everything else never changed. Hence 1kg is now 2%, therefore the total is 50kg.
Hmm, you can think of it this way:
If the water content is now 98%, that meams the fraction of the other material is 2% which is double, so the way to make it double is to either double the amount of the other material or halve the amount of water
Stage 1 - 1:99 ratio
Stage 2 - 2:98 => 1:49 ratio
The puzzle isn't solvable, because content is not the same as mass. That means that 99% of water can theoretically weigh 1 kg while the 1% potato 99kg. A more imaginable example to explain this would be an Iron Mug that is filled with water. The iron mug itself is very heavy. There's more water in the mug than iron. Even if I would empty the whole mug it wouldn't just half it's weight.
Content is frequently stated as percentage of the total mass, especially when water is involved, so your objection is irrelevant.
@@keith6706 -- Wrong! The person's objection is totally relevant, because the wording is inconsistent/fawlty. You are making excuses, and you are just hijacking the thread.
@robertveith6383 It's "faulty".
In the end there is 2% (100% - 98% = 2%) of dry matter.
Dry matter should still weigh exactly 1 kg (because it didn't evaporate) given by initial 100 kg * (100% - 99%) = 1 kg
The weight where 2% would be exactly 1 kg is 50 kg because 50 kg * 2% = 1 kg (thus 1 / 2% = 50)
This one reminds me of the Monty Hall 3 door problem in that almost everyone gets it wrong at first. The difference is that with the Monty Hall problem, many smart people still won't get it even after the answer is explained.
@@michaelhallock1428 I'm not a smart person and I do not get the Monty Hall problem but was able to solve this one easily.
People get the Monty Hall Problem wrong because the rules the host follows are not made clear:
The host must choose one of the two doors you didn’t choose
The host must choose a goat, and not a car
If you choose a car (probability 1/3), the host can choose either of the other doors, and you shouldn’t change
If you choose a goat (probability 2/3), the host must choose the other goat, and you should change
Therefore there is a 2/3 probability that changing the door is a good idea.
If the host chose another door at random and it happened to be a goat, then the correct answer is different. In that scenario, it makes no difference whether you change.
Yeah, the Monty Hall scenario fucks with your mind!
@@katrinabryce Wait, so the host always chooses the door with the other goat if you've chosen the door with the goat? So the host knows what is behind the door that you've chosen and knows also what is behind each of the other doors and knowingly chooses the door with the other goat? And in the case that you've chosen the door with the car he also knows that it is the door with the car and chooses one of the other doors randomly, knowing there will be a goat behind either door?
I hardly remember the problem and my questions are based almost entirely on the comment of your I'm replying here. So there is likely no use in properly explaining the "Three Door Problem" to me. I'd be intersted in a confirmation or correction of the things I've written above.
@@camelopardalis84 Yes, that is correct. And the reason people give the wrong answer is because this isn't made clear in the question, and people assume the host chooses another door at random. Knowing that it isn't a random choice is key to the calculation.
This is why I hate word math problems. If you lose 1% water weight, that will affect the "dry" part of the watermelon. Thus, the dry part wouldn't be the same. Doing this in real life would yield different results.
I have a barrel of water. The barrel itself weighs 1kg, the water in it weighs 99kg. The barrel is open at the top and 1% of the water has evaporated.
Are you saying the barrel of water will weigh 50 kilograms?
No. According to your interpretation, the barrel of water would weigh 99.01kg.
However, the problem is formulated somewhat differently. It is not stated that 1% of the water evaporated, but rather that the percentage of water in the total volume decreased by 1, which significantly changes the situation.
Let me try to explain using your example:
Initially, in a barrel weighing 1kg, there were 99kg of water - this means that the ratio of water to the total mass was 99 to 100 or 99%.
After 1% of the water evaporated(0.99kg), the ratio of water to the total mass became 98.01 to 99.01, or approximately 98.99%.
In order to achieve 98% water content in the total volume for two masses differing by 1 kg (the weight of the barrel), it is necessary to take 49 as the mass of water. In this case, the total mass will be 50, and the ratio will be 49 to 50, which is the solution to the problem.
I approached this by considering the difference in start weight (Xs) and end weight (Xe). Since the weight of melon solid doesn’t change, Xs-Xe=Ws-We, where Ws and We are the weights of water. We know Ws=0.99Xs and We=0.98Xe. Substitute in and rearrange to get 0.01Xs=0.02Xe. So Xe=1/2Xs=50kg.
But did your result answer the question asked? They asked the final weight, so the answer should be either 110 pounds or 490 newtons. kg is a unit of mass.
Come on dude, don't make it even more complicated
Leaving aside the fact that the pound is a mass unit, you are oversimplifying matters. Weight including or excluding the buoyancy force due to displaced air? Which definition of weight are you using? The latter could be significant in an accelerated environment such as the surface of the rotating earth. And that's only for starters... 😉😂
I deeply distrust percentages because they have betrayed my intuition a good number of times. So I went through it very rigorously and skeptically and arrived at the correct answer from the beginning. Maybe getting the correct answer or rather, not getting the incorrect answer without noticing, involves a good portion of knowing your limits.
I did it in only two simple steps:
1. the initial "dry" percentage is 1% of 100kg so that's 1kg.
2. the end "dry" percentage is 2%, so the total weight is 1kg / 2% = 50kg
"I deeply distrust (...) number of times."
I deeply distrust atoms. They make up everything!
the problem doesn't state whether the melon is 99% water by weight or by volume. Water may have a different relative density than the other components of the watermelon.
It's a simplified hypothetical, not an actual physical sitituation. It's implied from the context that 99% refers to kilograms, and that's enough. Asking if it's by weight or by volume is either unnecessary pedantry or inability to understand context. Also, you should have said "mass", not "weight", because those are different things in physics - if you want to be nitpicky, don't leave yourself open for nitpicking.
@@johncheshirsky8822 -- *No, it is not enough. The wording is flawed/inconsistent.*
@johncheshirsky8822 You're right.
Why does a drop of 1 percent in the water result in half the water being removed ?
Think of it as the dry weight doubling from 1 to 2 percent, but remaining at 1kg. So the total weight must be halved resulting in a large amount of water weight being lost.
When I first encountered this (with potatoes instead of watermelon) all I could think of is how this must be one long train ride and that the potatoes would rot before losing that much moisture, and that it on a cellular level, losing moisture must be way more complex than it is in this brain teaser. But that it is exactly that, a brain teaser, and the laws of the real world don't apply.
The question is confusing because you don't know what the 98% is referring to. 98% of the original whole or 98% based on the end ratio.
It means "98% water by mass." The total mass is M, and the mass of the water is W, and the mass of the watermelon rind is R. M = W + R, and 0.99M = W, and 0.01M = R.
@@wiggles7976 That formula works but, the interpretation opens a bit after dropping to 98%
W = 0.99, R = 0.01 thus M = 1 Okay W/M = 0.99 (99%)
Does the formula become
W/M(initial) = 0.98 (98%) thus W = 0.98 R = 0.01 M(new) = 0.99
or
W/M(new) = 0.98 (98%) thus W = 0.49 R = 0.01 M(new) = 0.5
It depends entirely on the frame of reference.
@@Kitasia if the water content changes, the ratio has changed. the water content of an object in the presence has no dependence on the ratio of that object in the past. W is W(new). W(new)/M(initial) bears no connection to reality. M is always solids + water. changing the water content changes M.
I did it a little differently. If the starting weight is 100kg and the water weight is 99% of that (99kg), the ratio is obviously 99(water)/100(total). If we lose water weight, we lose it from both measures, so (99-x)/(100-x) = 0.98.
(99-x)/(100-x) = 0.98
99-x = 0.98(100-x)
99-x = 98-0.98x
1 = 0.02x
100 = 2x
50 = x
Without knowing the mass of the "dry" portion, the question can't be answered.
But you know the mass of the "dry" portion (or at least can calculate it without problem). It is stated that the total weight at the beginning is 100kg and that the water at the beginning is 99% of total weight. It's a basic elementary school calucation to calculate the non-water mass
@@alam5055honestly i didnt take it as water makes up 99% of the weight but true
@@alam5055 It depends on how you read it, it says that water is 99% of the total content, which I would take as by volume. That last 1% of volume could be like uranium or something.
I solved it by solely considering the dry weight, since it is a fixed value. Both in the beginning and end, we have 1kg of dry weight. However, this same dry weight which accounted for 1% of the initial weight now accounts for 2% of the final weight. If 1kg is 2% of the final weight, then I multiply that by 50 to get 100%, which equals 50kg.
Lately, the "unsolvable" math questions have been more "poorly written" questions.
I wouldn't consider this one to be "poorly written" though.
@@DaSquyd exactly. Nor does it pose itself to be "unsolvable", more like "unintuitive". "Tricky" at worst. But that's the whole point.
Absolutely 💯 agree.
@@DaSquyd -- You missed understanding how it is poorly written.
@@robertveith6383 I mean, I must have since I solved the puzzle.
I think the most straightforward way to describe this trick (for me at least) is just looking at the dry weight (I suppose pretty much like your graphical demonstration but kind of in reverse?)
The reason I'm calling it a trick, I don't think its a riddle or a puzzle, is because the only thing that's difficult to understand is the phrasing of 99% vs 98% water content. Intuitively we look at that and think "small change". but if you had just phrased the problem in a more straightforward way; something like "if the fraction of dry mass doubles due to loss of water, how much water was lost?" most people's intuition would jump to something pretty close to the correct solution.
A 1% loss of $100 is NOT equal to $50. Stay safe out there in the real world.
Your example does not align with the intent of this flawed riddle.
I worked it out by saying 1kg of dry weight of the original represents 1% of the total weight. After the journey, that 1kg represents 2% of the total weight (100 - 98). So 1kg = 2/100 x the final weight w. 1kg = 1/50w means total weight is 50 kg
Let's be honest; In order to arrive at 50%, the question should really be reworded.
You do not arrive at 50%. It's 50kg.
Why does dry waste has to remain unchanged? If the overall weight goes down, won't the dry weight go down as well?
IMO, this is more of a wording issue than mathematical
No it isn't
if you think of it in ratios it is very obvious. if you conclude that dry is a constant, it is simple. it goes from 99%, which is 99:1 (99+1=100). Then it goes to 98%, which is 49:1 (49+1=50).
This principle is common in gambling. if you are getting a 99% chance of victory, the payout is 99:1 odds.
if the chance of victory drops to 98%, the odds go to 98:2, which reduce to 49:1.
I have a problem with you initially stating that "their water content was 99%" and then later at 3:33 you say "water is 99% of its weight". Content and weight (actually mass) are different things entirely. The question is flawed.
It's a math problem, not a physics one, and it's defiinitely not a real life situation. It's basically just asking you to solve an equation, the whole watermelon stuff is just irrelevant fluff. So it's completely normal for it to use colloquial language, instead of precise physical terms, *and* it's pretty damn easily understood from the context that it refers to the weight. It's like asking for specific geographic coordinates of point A and point B from an elementary or middle school math book, to see if there are any turns, road crossings, railroad works, or bridges/bodies of water on the way of the train, to see if something may slow it down, or what th weather conditions are like, etc. It's just a hypothetical train going from a hypithetical point A to hypothetical point B on a hypothetical stretch of a straight line. No need to overthink it this much.
The only plausible interpretations of "content" are percentage by mass, or percentage by volume. Since we aren't given the necessary information (i.e. density) to do volume calculations, it seems prudent to assume that "content" refers to mass.
In an exam situation, one could simply state this assumption before answering the question.
@@johncheshirsky8822 -- *No, you're wrong.* The original poster in this thread is correct. Your overly long post with its tangential remarks just made excuses for this fawlty problem.
Your post was reported as misinformation. It is best for you not to make posts like this.
Thank you for your accurate post.
@@weevilinabox -- No, in an exam situation, besides this Fawlty problem, it had better use the proper terminology consistently throughout the statement.
Mkay. I think it boils down to "there is always 1 kg of plant"
0.99 = water / (water + plant); solve for water, get 99kg of water and 100 kg total.
0.98 = water / (water + plant), solve for water, get 49kg of water and 50 kg total.
I got 50kg... Thanks for making me feel smart again Presh🤣
Usually even if I don’t get these I understand the answer pretty quick, but this took until the example with the dots before it made sense.
It's a poorly worded question.
Correct.
What is the correct wording.
I have solved it quickly with a method very similar to your latest solution. If 1kg dry part was 1% but becomes 2%, then 100% will be 50kg, which results 49kg of water. Q.e.d
Talk to any finance guy (I'm an engineer, not a finance guy) about bond coupons and bond prices on secondary markets.
Assume the prevailing interest rate is 1%. Someone issues a long term bond, with a $100 face value, and a 1% yield, which means that every year you will get a $1 coupon payment. Next year the inflation goes up, and the market will demand a 2% yield. What will be the price of the bond? Well, the bond will be traded for $50, because this way the $1 payment (the promised coupon) will mean a 2% yield, as demanded by the market. Obviously this will is a simplification (time to maturity, how sound is the issuer, and so on), but it is exactly the same idea.
Ah yes, "difficult" math is now the same as poorly worded sentences.
This is one of the first things we do as chemical engineers. The key is to do the calculations on the amount that does not change - i.e., the 'dry' mass.
I always did this one in my head. Originally the dry melon 1 kg was 1% of the whole; now that same 1 kg is 2% of the whole. So how much do you have to multiply that 2% to get up to 100%? 50.
I have a feeling it would've been harder if the number is weren't so easy to keep in your head.
Much simpler is that at the end we know 1kg dry weight is 2% of the total so just divide 1 by 0.02 No need to draw dots to visualise that.
I don't consider myself particularly good at maths, but my mind went straight to: "From the initial condition it is obvious that the non-water weight is 1kg. In the end that 1kg is 2% of the total weight, so the total weight must be 50kg. I guess that is similar to the 'dots' method, but without the dots 🙂
An easier way to visualize this is to look at the DRY WEIGHT. At first, it's 1%. It DOUBLES to 2%. The only way this could happen is if the water weight was cut in half. So 100kg at 1% becomes 50kg at 2%. What a fantastic puzzle!!!