A 30-litre mixture of milk and water contains 15% water. How much water must be added to it to increase the percentage of water in the solution to 37.5%?

A 30-litre mixture of milk and water contains 15% water.

initial quantity of water in the mixture = 30 of 15%

= $$30\times\ \frac{15}{100}$$

= 4.5 litre

initial quantity of milk in the mixture = 30-4.5

= 25.5 litre

Let's assume 'y'litre water added to make the quantity of water 37.5% in the new mixture.

$$\frac{25.5}{4.5+y}\ =\ \frac{100-37.5}{37.5}$$

$$\frac{25.5}{4.5+y}\ =\ \frac{62.5}{37.5}$$

$$\frac{25.5}{4.5+y}\ =\ \frac{5}{3}$$

$$\frac{5.1}{4.5+y}\ =\ \frac{1}{3}$$

4.5+y = 15.3

y = 15.3-4.5

= 10.8 litre