Question

A vessel is filled with liquid, which is 3 parts water and 5 parts milk. How much of the liquid should be drawn of and replaced by water to make it half water and half milk?

Answer 1

Final/initial = (1-replace/total)^n
1/2/(5/8) = 1-k
4/5 = 1-k
K = 1/5

2nd method
Mixture drawn out and added water, it means syrup part only is added to water so
Let x be d mixture drawn out
3/8 + 5/8x = 1/2
5/8x = 1/8
x = 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