A vessel is filled with liquid, 3 parts of which are water and 5 parts syrup

A vessel is filled with liquid, 3 parts of which are water and 5 parts syrup. How much of the mixture must be drawn off and replaced with water so that the mixture may be half water and half syrup?

  1. 1/4 
  2. 1/3
  3. 1/7
  4. 1/5

Answer

Suppose the vessel initially contains 8 litres of liquid. Let x litres of this liquid is replaced with water.

Quantity of water in new mixture = 3 - 3x/8 + x

Quantity of syrup in new mixture = 5 - 5x/8

In new mixture, both water and syrup are equal.

3 - 3x/8 + x = 5 - 5x/8

x = 8/5

Part of mixture replaced = 8/5 * 1/8 = 1/5

The correct option is D.