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?

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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