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?

**SOLUTION**

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.

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?

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 = 10lbsAFTER EVAPORATION:

4.9lbs WATER + 0.1lbs OTHER = 5lbsAh very clever, good puzzle well explained. Love solutions to puzzles that seem impossible until the maths blows through it effortlessly haha

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… Read more »

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.

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

Hello Moronski. Can you elaborate more on your concern? What do you think the correct answer is?

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.

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… Read more »

The equation is simply:

0.1/(10 – X) = 2%

Therefore, X = 5lbs.

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.

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

Can you please elaborate.

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