Question

A vessel filled with a liquid, 3parts 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?​

Answer 1

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

Answer 2

Suppose the vessel initially contains 8 liters of liquid.

Let x liters of this liquid be replaced with water.

Water in new mixture = (3-3x/8+x)

Syrup in new mixture = (5-5x/8)

Then (3-3x/8+x) = (5-5x/8)

5x + 24 = 40 - 5x

10x=16

==>x=8/5

So part of mixture replaced is 8/5*1/8=1/5