A container with a capacity of 90 litres is initially filled completely with pure milk. First, 9 litres of milk is removed and replaced with an equal amount of water. Then, 9 litres of this new mixture is taken out and replaced again with water. What is the volume of pure milk remaining in the final mixture?

Explanation

Let the total volume of milk at the start be T litres. When y litres of the mixture is removed and replaced with water n times, the remaining quantity of pure milk is given by ((T - y) / T)^n × T. Here, T = 90 litres, y = 9 litres, and n = 2. Therefore, the amount of pure milk left is ((90 - 9) / 90)^2 × 90 = 72 litres.