Cucumber paradox

Algebra Level 2

Suppose that you go out and buy 100 lbs. of cucumbers, that are 99% water. Unfortunatly, you do not observe the rules of caring for your cucumbers so after some time, they dehydrate until they are only 98% water. How much do they then weigh?


The answer is 50.

Robert Sardoma by Robert Sardoma , 35, Philippines

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2 solutions

Andreas Wendler
Mar 2, 2016

Initially one cucumber (C) consists of water (W) and substance (S) where W=0.99 C means C=0.99 C+S (a).

For cucumbers (C1) after dehydration value S remains constant and we have: C1=0.98*C1+S (b).

Difference (a) - (b) delivers C-C1=0.99 C-0.98 C1 => 0.01 C=0.02 C1 => C1=1/2*C => weight will be the half!

4 Helpful 0 Interesting 0 Brilliant 1 Confused
Pradeep Tripathi
Jan 4, 2019

If original cucumber that we bought gets either hydrated or dehydrated, its static weight (weight of dry cucumber) would be constant.

So, solving equations by considering the above logic ,we will get 50 lb as answer of the given problem

0 Helpful 0 Interesting 0 Brilliant 0 Confused

It would be nice if you "solve those equations" and show it

Jake Tricole - 1 year, 9 months ago

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