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8 litres are drawn from a cask full of wine and is then filled with water. This operation is performed three more times. The ratio of the quantity of wine now left in cask to that of water is 16 : 65. How much wine did the cask hold originally?

A.
18 litres
B.
24 litres
C.
32 litres
D.
42 litres

1 Answer

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Answer is C

Let initial quantity of wine =x litre

After a total of 4 operations, quantity of wine
$ x(1-\frac{y}{x})^{n} => x(1-\frac{8}{x})^{4}$
Given that after a total of 4 operations, the ratio of the quantity of wine left in cask to that of water = 16:65

$ \frac{x(1-\frac{8}{x})^{4}}{x} = \frac{16}{81}$

$ (1-\frac{8}{x})^{4} = (\frac{2}{3})^{4}$

$ (1-\frac{8}{x}) = \frac{2}{3}$

$ (\frac{x-8}{x}) = \frac{2}{3}$

3x - 24 = 2x

x = 24

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