A cask full of wine from which 8 litres are drawn and is then filled with water. This operation is performed three more times. The ratio of quantity of wine left in the cask to that of the water is 16: 81. How much wine did the cask hold originally?

42 litres
32 litres
24 litres
18 litres

Correct Answer: 24 litres

Explanation:

Let A liters wine cask hold originally, then
A[1 - (8 / A)]4 / A = 16 / 81
⇒ (1 - (8 / A))4 = (2 / 3 )4
⇒ (1 - (8 / A)) = (2 / 3)
⇒ (8 / A) = (1 - (2 /3))
⇒ (8 / A) = (1 / 3)
∴ A = 24 liters

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