A 24 liters of milk and water mixture contains milk and water in the ratio 3: 5. What litres of the mixture should be taken out and replaced with pure milk so that the final mixture contains milk and water in equal proportions?

Question: A 24 liters of milk and water mixture contains milk and water in the ratio 3: 5. What litres of the mixture should be taken out and replaced with pure milk so that the final mixture contains milk and water in equal proportions?

Solution:
In 24 l of mixture, milk = (3/8) × 24 = 9 L
So water = 24 - 9 = 15 L
Now since the mixture is to be replaced with pure milk, the amount of mixture will remain same after replacement too.
In 24 L mixture, to have 12 L water and 12 L milk, 3 L of water should be taken out, since we are only adding milk.
Let x L of mixture taken out.
So (5/8) × x = 3
⇒ 5x = 24
Solve, x = 24/5 L