Nine litres of solution are drawn from a cask containing water. It is replaced with a similar quantity of pure milk. This operation is done twice. The ratio of water to milk in the cask now is 16:9. How much does the cask hold?

**Solution**

Let there be x litres in the cask.

After n operations,

Water left in vessel / Original quantity = (1 – 9/x)^{n}

16/25 = (1 – 9/x)^{2}

4/5 = 1 – 9/x

∴ x = 45 litres.