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    Question

    12 litres are drawn from a cask full of wine and is then

    filled with water. This operation is performed one more time. The ratio of the quantity of wine now left in cask to that of the water is 4:5. How much wine the cask hold originally?
    A 24 litres Correct Answer Incorrect Answer
    B 48 litres Correct Answer Incorrect Answer
    C 36 litres Correct Answer Incorrect Answer
    D 15.75 litres Correct Answer Incorrect Answer
    E 56 litres Correct Answer Incorrect Answer

    Solution

    Let the quantity of the wine in the cask originally be x litres Then, quantity of wine left in cask after 2 operations = [x {1 - (12/x)}2] litres Therefore, [x {1 - (12/x)}2 /x] = 4/9 [1 - (12/x)}2 ] = (2/3)2 x = 36 Original quantity of cask = 36 litres

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