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?

• (a) m = n — Correct. After transferring 20 ml milk to Y, container Y has 20 ml milk + 100 ml water = 120 ml mixture. When 20 ml is sent back, it contains milk and water in the same ratio; the amount of water left in Y equals the amount of milk left missing from X. Hence, milk proportion in X = water proportion in Y.
• (b) m > n — Incorrect. By conservation, the milk absent from X is exactly equal to the water absent from Y, so the corresponding proportions are equal.
• (c) m < n — Incorrect. Same reason: neither exceeds the other.
• (d) Cannot be determined — Incorrect. The result is definite and does not depend on extra data.

Key fact: In such exchange problems, the quantity of milk in water equals the quantity of water in milk after the round transfer. Therefore, m = n.