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Ratio

by talaangoshtari » Wed May 20, 2015 12:15 am
8 litres are drawn from a wine and is then filled with water. This operation is performed 3 more times. The ratio of the quantity of water now left in cask to that of the wine is 65:16. How much wine did the cask hold originally?

A.24
B.30
C.45
D.63
E.70
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by GMATGuruNY » Wed May 20, 2015 3:42 am
I believe that the following represents the intent of the problem:
talaangoshtari wrote:8 liters are drawn from a cask full of wine. The cask is then filled with water. This operation is performed 3 more times. After the four operations, the ratio of water to wine in the cask is 65:16. How much wine did the cask hold originally?

A.24
B.30
C.45
D.63
E.70
After 4 operations, wine/water = 16/65.
Since 16+65 = 81, wine/total = 16/81 = (2/3)�.

The value in red indicates the following:
After each of the 4 operations, 2/3 of the wine REMAINS, implying that 1/3 of the wine was REMOVED.
Thus, the 8 liters removed with each operation must be equal to 1/3 of the total volume:
8 = (1/3)x
x = 24.

The correct answer is A.
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