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?
Answer & explanation
Answer: (a) m = n
After the two transfers each container again holds 100 ml. Whatever water went into X must be matched by the same amount of milk left in Y, so X’s milk share equals Y’s water share: m = n = 5/6.
- After the first transfer: X has 80 ml milk; Y has 100 ml water + 20 ml milk = 120 ml.
- 20 ml of Y’s mixture carries 20 × 20/120 = 10/3 ml milk and 20 × 100/120 = 50/3 ml water back to X.
- X: milk = 80 + 10/3 = 250/3 ml out of 100 ml, so m = 5/6.
- Y: water = 100 − 50/3 = 250/3 ml out of 100 ml, so n = 5/6.
- So m = n.
Remember · Back-and-forth transfers of equal volume: the milk in the water jar always equals the water in the milk jar.
Question and answer: UPSC's official GS Paper II (2022, Series A) — paper ↗ · answer key ↗. Explanation: Minimalist IAS, checked 30 Sept 2026 (how we verify). ·