Mixtures Alligation

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 water is 16 : 65. How much wine did the cask hold originally?

  1. 18 litres
  2. 42 litres
  3. 32 litres
  4. 24 litres

Solution

Let the quantity of the wine in the cask originally be x litres. 8 litres of wine is removed from it and replaced with water. This operation is done total 4 times. After 4 operation,

Wine : Water = 16 : 65 or Wine : Total = 16 : 81

[(x-8)/x]4 = 16/81

(x-8)/x = 2/3

3x - 24 = 2x

x = 24

The correct option is D.