Two containers contain a mixture of milk and water. In one container, the ratio of milk to water is 4 : 1 and the ratio of milk to water in the other container is 1 : 3. 10 litres of mixture from the first container and 16 litres of mixture from the second container is mixed together in a third container, already containing some amount of pure milk. In the new mixture, it was found that the ratio of milk to water was 3 : 2. Find the volume of the new mixture.

The first container has milk and water in a 4 to 1 ratio, so taking 10 litres gives 8 litres of milk and 2 litres of water. The second container has a 1 to 3 ratio, so taking 16 litres gives 4 litres of milk and 12 litres of water. Combining these two gives a total of 12 litres of milk and 14 litres of water, making the intermediate mixture exactly half milk and half water. To achieve a final 3 to 2 ratio of milk to water after adding pure milk (which contains no water), the total water must be 14 litres, meaning the final mixture must contain 21 litres of milk. Since 12 litres of milk are already present, 9 litres of pure milk are added to the 26 litres of combined mixture, resulting in a new mixture volume of 35 litres.

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