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The ratio of water and milk in a mixture of 65 liters is 5:8. What quantity of water(in liters) must be added so that the ratio of water and milk becomes 3:4?

Let's call the quantity of water in the mixture x liters.

The quantity of milk in the mixture is 65-x liters.

The ratio of water to milk in the mixture is currently 5:8, or 5/(5+8) = 5/13 of the mixture.

The ratio of milk to water in the mixture is currently 8:5, or 8/(5+8) = 8/13 of the mixture.

Amount of water in mixture = (5/13) × 65 litre

⇒ 25 liters

Amount of milk in mixture = (8/13) × 65

⇒ 40 liters

We want the ratio of water to milk to be 3:4, or 3/(3+4)=3/7 of the mixture.

Since the quantity of the mixture is not changing, the ratio of the components must remain constant. Thus, the ratio of water to the mixture must be 3/7 of the mixture when we add the water.

(25 + x)/40 = 3/4

⇒ 100 + 4x = 120

⇒ 4x = 20

⇒ x = 5