52. 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 the water
is 16 : 65. How much wine the cask hold originally ?
A. 18
litres B. 24 litres
C. 32 litres D. 42 litres
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Answer:
Let
the quantity of the wine in the cask originally be x litres
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then,
quantity of wine left in cask after 4 operations
= [x(1- 8/x)4] litres.
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Therefore x(1-
8/x)4 / x =
16/81 =› (1- 8/x)4 = (2/3)2
=› (x - 8 / x) = 2/3 =› 3x - 24 = 2x =› x =
24.
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