6 litres are drawn from a cask full of wine and it is then filled with water. 6 litres of the mixture are drawn and the cask is again filled with water. The quantity of wine now left in the cask to that of water is 12:23. How much does the cask hold?

54 litres
62 litres
70 litres
72 litres

Correct answer: 54 litres

Solution

If the cask capacity is $V$ litres, after the first replacement the wine left is $V-6$. After the second withdrawal and refill, wine left becomes $(V-6)^2/V$. Given wine : water = 12 : 23, wine fraction is $12/35$, which leads to $(1-6/V)^2 = 12/35$ and gives $V = 54$ litres.

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