Explanation:

Container X contains 100 ml of milk and container Y contains 100 ml of water.
If 20 ml of milk transferred from container X to container Y, then:
Amount of milk left in container X = 100 – 20 = 80 ml
Amount of solution in container Y becomes = 100 ml water + 20 ml milk = 120 ml
Ratio of milk and water in container Y = 20 : 100 = 1 : 5
Amount of milk in 20 ml solution of container Y = (1/6) × 20 = 3.33 ml
Amount of water in 20 ml solution = 20 – 3.33 = 16.67 ml
If 20 ml of this solution is transferred from container Y to container X, then:
Amount of solution in container X becomes = (80 + 3.33), i.e. 83.33 ml milk + 16.67 ml water
Amount of solution in container Y becomes = (100 – 16.67), i.e. 83.33 ml water + (20 – 3.33), i.e. 16.67 ml milk
As per the question, m denotes the proportion of milk in X, and n denotes the proportion of water in Y.
So, m = 83.33 ml and n = 83.33 ml
Thus, m = n