There are two containers X and Y. X contains 100 ml of milk and Y contains 100 ml of water. 20 ml of milk from X is transferred to Y. After mixing well, 20 ml of the mixture in Y is transferred back to X. If m denotes the proportion of milk in X and n denotes the proportion of water in Y, then which one of the following is correct?

Correct Option: m = n

Container X has 100 ml milk, Y has 100 ml water. 20 ml milk from X is transferred to Y. Now Y has 100 ml water + 20 ml milk = 120 ml total, with milk proportion = 20/120 = 1/6, and water proportion = 100/120 = 5/6. Now 20 ml of this mixture is transferred back to X. The transferred 20 ml mixture contains: milk = 20 × (1/6) = 10/3 ml, water = 20 × (5/6) = 50/3 ml. Container X now contains: milk = 100 - 20 + (10/3) = 80 + 3.33 = 83.33 ml, and water = 50/3 ml. Total volume in X = 100 ml. Proportion of milk in X (m) = 83.33 / 100 = 5/6. Container Y now contains: remaining mixture = 120 - 20 = 100 ml. Since 20 ml was removed, the proportion of water in Y remains unchanged at 5/6. Thus n = 5/6. Therefore, m = n.