In a mixture of 45 litres, the ratio of milk and water is 3 : 2, How much water must be added to make the ratio 9 : 11?Options :10 litres15 litres17 litres20 litres

To solve this problem, we first need to understand the initial ratio and volume of the mixture.

The initial ratio of milk to water is 3:2. This means that out of every 5 parts of the mixture, 3 parts are milk and 2 parts are water.

The total volume of the mixture is 45 litres. We can divide this total volume by the total parts to find the volume of one part.

45 litres ÷ 5 parts = 9 litres/part

So, in the initial mixture, the volume of milk is 3 parts × 9 litres/part = 27 litres, and the volume of water is 2 parts × 9 litres/part = 18 litres.

We want to add water to make the ratio of milk to water 9:11. This means that out of every 20 parts of the new mixture, 9 parts are milk and 11 parts are water.

The volume of milk remains the same at 27 litres, which is 9 parts. So, one part in the new mixture is 27 litres ÷ 9 parts = 3 litres/part.

Therefore, the volume of water needed to make 11 parts is 11 parts × 3 litres/part = 33 litres.

Since we already have 18 litres of water in the mixture, we need to add 33 litres - 18 litres = 15 litres of water.

So, the correct option is 15 litres.