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Watering the wine

Watering the wine

A liter is extracted from a 5-liter carafe filled with wine and replaced with a liter of water. It mixes well and after a while a liter of the mixture is removed again and then a liter of water is put back, so that the carafe is still full. Finally we take another liter of liquid out of the carafe and fill with another liter of water.

A mixture of water and wine will remain in the carafe. What is more, wine or more water?

Solution

Every time we do the operation of adding a liter of water, eliminating a liter of the mixture, we are reducing the percentage of wine by 4/5, since we remove 1/5 of what there is, and it is replaced by water.

After the first step, there will be 4/5 of wine. After the second step, (4/5) * (4/5) = 16/25, and in the third step we will get (16/25) * (4/5) = 64/125, which represents little more than the half of the mixture, specifically 64/125 = 51.2%.
Thus Some more wine will remain.