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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?

Correct answer: B. 24 litres

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

Explanation

Four operations are performed, and each leaves the fraction (V - 8 litres) / V of the wine, where V is the original capacity. Since the final wine fraction is 16/(16 + 65) = 16/81 = (2/3)^4, we have (V - 8 litres)/V = 2/3, so V = 24 litres. The likely mistake is option c, 32 litres, from using only three operations instead of four.

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