How much of the mixture must be drawn off and replaced with water so that the mixture may be half water and half syrup?

Question

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?

Answer 1

3+5=8
(3-1)+(5-1)=8-2
2+4=6
(2+2)+(4+0)=6+2
4+4=8

Answer 2

Suppose the vessel initially contains 8 litres of liquid.

Let x litres of this liquid be replaced with water.

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

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

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

So 5x + 24 = 40 - 5x

10x = 16

x = 8/5 .

So, part of the mixture replaced = ( 8/5 x 1/8 ) = 1/5