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?

Sure, let's solve this step by step.

Step 1: Understand the problem The problem is about a mixture of milk and water. The current ratio of milk to water is 3:2 and the total volume of the mixture is 45 litres. We need to find out how much water needs to be added to change this ratio to 9:11.

Step 2: Calculate the current volumes of milk and water The ratio of milk to water is 3:2, which means for every 3 parts of milk, there are 2 parts of water. The total parts in the mixture are 3 (for milk) + 2 (for water) = 5 parts. So, 1 part of the mixture = 45 litres / 5 = 9 litres. Therefore, the volume of milk = 3 parts * 9 litres/part = 27 litres. And, the volume of water = 2 parts * 9 litres/part = 18 litres.

Step 3: Calculate the volume of water needed to change the ratio to 9:11 In the new ratio of 9:11, the volume of milk remains the same (27 litres), which corresponds to 9 parts. So, 1 part = 27 litres / 9 = 3 litres. Therefore, the volume of water needed to make the ratio 9:11 = 11 parts * 3 litres/part = 33 litres.

Step 4: Calculate how much more water needs to be added The current volume of water is 18 litres, and we need it to be 33 litres. So, the volume of water that needs to be added = 33 litres - 18 litres = 15 litres.

So, 15 litres of water must be added to the mixture to make the ratio of milk to water 9:11.