8 liters 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 did the cask hold originally?
18 liters
24 liters
32 liters
42 liters
Explanation:
Let the quantity of the wine in the cask originally be x liters.
Then, quantity of wine left in cask after 4 operations = $[x(1-(8/x) ^4] $liters.
=> $[x(1-(8/x) ^4]$/x = 16/81
=>$ (1-8/x) ^4$ = $(2/3) ^2 $
=> (x - 8)/x = 2/3
=> 3x - 24 = 2x
=> x = 24.