3 litres are drawn from a cask full of wine and are then filled with water. This operation is performed two more times. The ratio of the quantity of wine now left in the cask to that of water is 8: 19. How much wine did the cask hold originally?
Show answer & explanation
Correct answer: D
Explanation
Given:
Each time, 3 liters are drawn off and the same amount of water is added.
This process is repeated 3 times.
Finally, wine : water = 8 : 19
By the formula:
Finally, wine = Initial volume × (1 − drawn off/total)³
Let the total volume of the barrel = x liters
Finally, wine volume = x(1 − 3/x)³
Finally, total mixture = x
Hence,
Wine : water = 8 : 19
Wine's share = 8/27
x(1 − 3/x)³ = (8/27)x
(1 − 3/x)³ = 8/27
1 − 3/x = 2/3
3/x = 1/3
x = 9 liters