Silly maths question about heuristics

Question

A farmer owns $200$ kg of cucumbers that contain $99 \%$ water. After a day lying in the sun, the cucumbers only contain $98\%$ of water. How much kg does the farmer has now?

How silly it may seem I don't really understand why the answer is 100kg.

I know that in the beginning the remaining $1\%$ represents the 2 kg of the cucumbers and I'd think that $99\%$ which is water represents 198 kg of the cucumbers. So after a day the cucumbers contain $98\%$ of water and the remaining $2\%$ is the weight of the cucumbers and evaporated water so the new weight of the cucumbers is 198kg.

I don't know where I went wrong.

score 3 · Accepted Answer · answered Sep 26 '17 at 18:49

3

The only thing that is changing is the amount of water - the amount of cucumber stays the same. So as you rightfully concluded, there is initially 2kg of cucumber, and 198kg of water. Then this weight structure changes. You know there is still 2kg of cucumber, which now makes up 2% of the total mass. So from this, you can deduce that the total mass must be 100kg, since $$\frac{2kg}{2\%}=\frac{2kg}{0.02}=100kg$$

answered Sep 26 '17 at 18:49

John Doe

14,545

Oh, I realise now that the question tricked me. It's about the mass of the cucumbers not the water. Stupid of me. – Anonymous196 Sep 26 '17 at 18:52

Bram28 · Answer 2 · 2017-09-26T18:55:41.147

3

You did everything right until the very last step:

The $2$% of the total weight after the day is still the $2$ kg of 'non-water cucumber-stuff' from before, so the total weight of the cucumbers is 100kg

edited Sep 26 '17 at 18:55

answered Sep 26 '17 at 18:50

Bram28

100,612
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Silly maths question about heuristics

2 Answers2