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?

18 litres
24 litres
32 litres
42 litres

Correct Answer: 24 litres

Explanation:

Let the quantity of the wine in the cask originally be x litres.

Then, quantity of wine left in cask after 4 operations =	[	x	❨	1 -	8	❩	4	] litres.
					x

∴	❨	x(1 - (8/x))⁴	❩	=	16
		x			81

⟹	❨	1 -	8	❩	4	=	❨	2	❩	4
			x					3

⟹	❨	x - 8	❩	=	2
		x			3

⟹ 3x - 24 = 2x

⟹ x = 24.

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