From a cask of wine containing 25 litres, 5 litres are withdrawn and the cask is refilled with water. The process is repeated a second and then a third time. Find the quantity of wine left in the cask and also the ratio of wine to water in the resulting mixture.

61 : 64
16 : 46
46 : 16
64 : 61

Correct Answer: 64 : 61

Explanation:

Here, quantity of wine left after third operation
= [1 - (5 / 25)]³ x 25 = (4 / 5)³ x 25 = (64 / 125) x 25 = (64 / 5) = 12 ⁴/₅ liters.
Final ratio of wine to water = (64 / 125) / (1- 64 /125)
= (64 / 125) /(61 / 125)
Wine : Water = (64 / 61)

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