A vessel is full of pure milk. 9 litres are drawn out and replaced with water, and the operation is repeated once. The milk and water are now in the ratio $16 : 9$. What is the capacity of the vessel?

Explanation

1. 01

   Milk fraction now = $\frac{16}{16 + 9} = \frac{16}{25}$.

2. 02

   So $\left(1 - \frac{9}{C}\right)^2 = \frac{16}{25}$, giving $1 - \frac{9}{C} = \frac{4}{5}$.

3. 03

   $\frac{9}{C} = \frac{1}{5}$, so $C = 45$ litres.