X और Y, 300 m लम्बे वृत्तीय मार्ग में दौड़ते हुए 3 km की दौड़ लगाते हैं। उनकी चाल 3 : 2 के अनुपात में है। अगर उन्होंने एक-साथ एक ही दिशा में दौड़ शुरू की है, तो कितनी बार पहला व्यक्ति, दूसरे व्यक्ति के पास से गुजरेगा (दौड़ शुरू करने की स्थिति को पास से गुजरने में नहीं गिना गया है)?
Read this question in English
X and Y run a 3 km race along a circular course of length 300 m. Their speeds are in the ratio 3:2. If they start together in the same direction, how many times would the first one pass the other (the start-off is not counted as passing)?
(a) 2 · (b) 3 · (c) 4 · (d) 5
उत्तर और व्याख्या · explanation in English
Answer: (b) 3
By the time X finishes 3 km, Y has run 2 km, so X has gained 1000 m — three full laps of 300 m and a little more. Each full lap gained is one pass, so X passes Y 3 times.
- The race ends when X, the faster runner, completes 3 km = 3000 m.
- Speeds are 3 : 2, so in that time Y runs 2/3 × 3000 = 2000 m.
- X gains 3000 − 2000 = 1000 m on Y.
- X passes Y each time the lead reaches a whole lap: at 300 m, 600 m and 900 m. 1000 ÷ 300 = 3.33, so there are 3 passes.
Remember · On a circular track, passes = lead gained by the faster runner ÷ track length, counting whole laps only.
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). ·