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## Tea and Wine 7

You take a spoon of wine from a barrel of wine and put it into your cup of tea. Then you return a spoon of the (non-uniform) mixture of tea and wine from your cup and put it in the barrel. Now you have some foreign substance (wine) in the cup and some foreign substance (tea) in the barrel. Which is larger: the quantity of wine in the cup or the quantity of tea in the barrel?

they are equal

This is pretty counter-intuitive. Two steps take place: 1. You move a spoonful of wine from the barrel to the cup. 2. You move a spoonful of mixture from the cup back to the barrel.

After step 1, there is 1 spoonful of wine in the cup. In step 2, you move x tea into the barrel and (1-x) wine into the barrel. Therefore, in the cup, you have 1-(1-x) = x wine remaining. x = the amount of tea in the barrel.

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Submitted by
Ravi
over 7 years ago
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Difficulty 4.7 ?

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