Two vessels contain 39 litres and 51 litres quantity of solution contains milk and water in the ratio of 19 : 20 and 30 : 21 respectively. Now the solutions are mixed with each other, then how many litres of water to be added in the final solution to make the resulting solution in the ratio 1 : 1?

Given:

Vessel 1 contains 39 litres of solution with a milk to water ratio of 19:20.

Vessel 2 contains 51 litres of solution with a milk to water ratio of 30:21.

We need to add water to the final mixture to make the milk to water ratio 1:1.

Formula used:

Milk in Vessel 1 = (19/39) × 39 = 19 litres

Water in Vessel 1 = (20/39) × 39 = 20 litres

Milk in Vessel 2 = (30/51) × 51 = 30 litres

Water in Vessel 2 = (21/51) × 51 = 21 litres

The total milk and water in the final mixture.

Total milk = 19 (from Vessel 1) + 30 (from Vessel 2) = 49 litres

Total water = 20 (from Vessel 1) + 21 (from Vessel 2) = 41 litres

The amount of water to be added to make the ratio 1:1.

We want the final solution to have the same amount of milk and water, i.e., 49 litres of milk and 49 litres of water.

Currently, there are 41 litres of water, so the amount of water to be added is:

Water to be added = 49 - 41 = 8 litres

∴ 8 litres of water should be added to the final solution to make the milk to water ratio 1:1.