A drum holds 125 litres of pure milk. 25 litres are drawn out and replaced with water; this is done three times in all. What is the final ratio of milk to water?

Explanation

1. 01

   Each operation keeps $\frac{125 - 25}{125} = \frac{4}{5}$ of the milk.

2. 02

   Milk after three operations = $125 \times \left(\frac{4}{5}\right)^3 = 125 \times \frac{64}{125} = 64$ litres.

3. 03

   Water = $125 - 64 = 61$ litres, so milk : water = $64 : 61$.