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?
Aptitude
Alligation or Mixture
Choose an option
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A42 litres
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B32 litres
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C24 litres
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D18 litres
Answer
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