X और Y दो पात्र हैं। X में 100 ml दूध है और Y में 100 ml पानी है। X में से 20 ml दूध निकालकर Y में डाला जाता है। इन्हें अच्छी तरह मिलाकर, Y का 20 ml मिश्रण निकालकर वापस X में मिलाया जाता है। यदि X में दूध का अनुपात m से निर्दिष्ट होता है और Y में जल का अनुपात n से निर्दिष्ट होता है, तो निम्नलिखित में से कौन-सा एक सही है?
Read this question in English
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 · (b) m > n · (c) m < n · (d) Cannot be determined due to insufficient data
उत्तर और व्याख्या · explanation in English
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). ·