Cucumbers

You had 10lbs of cucumbers, each of which consisted of 99% water. After leaving them in the sun, some of the water in the cucumbers evaporated. If the cucumbers ended up with 98% water in them, how much of their weight did they lose?

The cucumbers lost half of their weight.

If the water was 99% of the total weight, the remaining substance must have weighed 0.1lbs. If after the evaporation the substance comprises 2% = 1/50 of the cucumbers, the total weight must be 50 x 0.1lbs = 5lbs.

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  1. We are familiar with the proposition that about 60% of the human body is water. This is not by weight, but by volume. Still, supposing the truly unearthly “cucumbers” proposed were not so described, but possessed 99% of their substance by weight, then it would be both reasonable and necessary to state this in the problem. There is no such statement, nor is there a statement of any kind relating the water percentage to weight: the rest of the “cucumbers” could be oganesson (if briefly), adamantine, or polystyrene, or indeed fibre, as one previous objector more reasonably noted. The question is irrelevant to a solution of the puzzle, the point being that the “solution” does not describe the state of the final cucumbers via a water-loss transition, but gives two entirely unrelated situations. It is in fact no solution at all, given that it is based on, and requires an unevidenced assumption that the 1% of the cucumber that is not water has a weight that can be inferred. It cannot. Still, to make the leap that the solution requires and to arbitrarily assume that the 99% water content refers to a weight, the weight of 99% of the original “cucumbers” is 9.9lbs. If the water content is reduced to 98% OF THE SAME cucumbers, then a weight loss of just over 0.1 lbs has occurred (1% of 99% of 10lbs) and the weight of the remaining cucumbers (real world cucumbers this time) is most certainly a little below 9.9lbs. The non-water remainder still weighs 0.1lbs, and with most of the water intact the weight of the cucumbers most certainly has not fallen by half! In fact. But what are facts, this is puzzleland.

    1. Hi Element, thank you for your input. Generally, only 95% of a cucumber is water (in terms of weight), so indeed, the puzzle is not biologically correct. Nevertheless, we feel the formulation is understandable. When we say that the cucumbers are left with 98% of water in them, this suggests that we are referring to the final weight, not the starting weight.

      1. The formulation is indeed very easily understandable, but the ratio between water and other content in terms of the contributing weight of either item (i.e., not in terms of percentages) is not stated in the puzzle and is non-inferable. The given solution is wrong, or, alternatively, ANY solution at all is possible, not merely the single one given.

        1. The solution is correct, assuming the percentages refer to the weight of the nutrients. People generally do not have issues with the formulation. Only weight is referenced in the problem and as you said, if the percentages refer to volume, the problem is unsolvable.

  2. Am i right in thinking this is more of a wordplay riddle than a maths riddle? You’re saying that the weight of the water in the cucumbers aren’t actually part of the cucumbers?

    1. Hi Matt. I would say it is a rather rigorous math exercise. The water inside the cucumbers is part of them, until it evaporates. Think about it like this:
      BEFORE EVAPORATION: 9.9lbs WATER + 0.1lbs OTHER = 10lbs
      AFTER EVAPORATION: 4.9lbs WATER + 0.1lbs OTHER = 5lbs

      1. Ah very clever, good puzzle well explained. Love solutions to puzzles that seem impossible until the maths blows through it effortlessly haha

  3. I noticed a flaw in your answer. There is 99% water inside the 10 lbs of cucumbers. From logic we can conclude that there is 1% of another substance (I say fiber), which can also be written as 1/10th of a lb of fiber. When the water percentage decreases by 1%, the fiber stays the same. There is still 1% of fiber in the 10lbs of cucumbers.
    I believe the true answer is that the cucumbers lost 1% (or 1/10th of a lb) of water.

    Note: Just from pure observation, we can conclude mathematically that there is absolutely no way that 1% of these 10lbs of cucumbers equals 5lbs.

    1. Hi Dawson. If the final weight of the cucumbers is 9.9lbs, then the water would comprise 9.8/9.9 ~ 98.(98)%. The answer is counter-intuitive, but if you make the calculations carefully, you will see it is correct.

  4. That 10 Ibs of CUCUMBER “CONSISTED” of 99% water. You can’t suddenly change your mind and look at cucumber as 1% of itself. Maybe you can take mathematics out of logic, but you can’t take logic out of mathematic, you’ve got lost in the translation mate

      1. 50% stays on a bench, 50% smells all over the kitchen – all together = almost 5kg. Ok, ok, now you know why I named myself Moronski.

  5. I’m calling bull.
    So in your equation your saying that 9.9 lbs of water weight subtract how much weight was lost (being X) would be equal to 10 lbs of overall weight subtract how much weight was lost (being X) multiplied by a how much water weight there was? The problem is that you don’t just randomly multiply how much water weight is left, that’s dumb. You over complicated something to try and appear intelligent. If we are trying to solve how much weight is lost we write the equation as follows.
    10lbs of total weight – X = 9.9lbs of water weight + 0.1 lds of other weight -X
    Your formula does not apply to this situation.
    You should delete this question.

    1. An easy way of thinking about it is this:
      Pre-sun: 99% water and 1% plant stuff.
      After-sun: 98% water and 2% plant stuff.

      In this case you’ve lost so much water that your ratio has changed by 1%. You’ve doubled your plant stuff(1% to 2%). The only way to double your plant stuff is to reduce your water mass by half. So you once had 10lbs of cucumbers now you have 5lbs of cucumbers. You lost 5lbs of water and you haven’t lost any plant stuff.

      1. Assuming water is lost and the remainder remains constant
        99% => water 99 : 1 other (total 100)
        98% => water 49 : 1 other (total 50)
        Therefore 50 percent lost

    1. Of course. Since the cucumbers weigh 10 lbs in total, then the amount of water in them is 9.9 lbs. If X lbs of water evaporate, then we would have 9.9 – X lbs water and 10 – X lbs total weight. Now we write the equation:
      9.9 – X = 0.98 * (10 – X)
      This is a linear equation, so we solve it and get:
      0.1 = 0.02 * X => X = 5 lbs