A jar full of milk contains 50% water. A part of this milk is replaced by another milk containing 20% water and now the percentage of water was found to be 32%. The quantity of milk replaced is:

Question: A jar contains a milk-water mixture in which water is 50%. A part of the mixture is removed and replaced with another mixture containing 20% water. If the final mixture contains 32% water, what fraction of the original mixture was replaced?

Solution:
Let the total quantity of the mixture be 1 litre.
Suppose x litre of the mixture is removed and replaced.

Water remaining from the original mixture
= 50% of (1 - x)
= 0.50(1 - x) litre

Water added with the new mixture
= 20% of x
= 0.20x litre

∴ the total quantity of water in the final mixture
= 0.50(1 - x) + 0.20x

According to the question,
0.50(1 - x) + 0.20x = 0.32
⇒ 0.50 - 0.50x + 0.20x = 0.32
⇒ 0.50 - 0.30x = 0.32
⇒ 0.30x = 0.18
⇒ x = 0.18/0.30
⇒ x = 3/5

Therefore, 3/5 of the original mixture was replaced.