दो व्यक्ति A और B किसी वृत्तीय मार्ग पर दौड़ रहे हैं। प्रारंभ में B, A से आगे है तथा उनकी स्थितियाँ वृत्त के केन्द्र पर 30° का कोण बनाती हैं। जब A, उस बिन्दु पर पहुँचता है जो कि उसके प्रारम्भिक बिन्दु से व्यासतः सम्मुख है, तब वह B से मिलता है। A और B की चालों में क्या अनुपात है, यदि वे एकसमान चाल से दौड़ रहे हैं?
Read this question in English
Two persons, A and B are running on a circular track. At the start, B is ahead of A and their positions make an angle of 30° at the centre of the circle. When A reaches the point diametrically opposite to his starting point, he meets B. What is the ratio of speeds of A and B, if they are running with uniform speeds?
(a) 6: 5 · (b) 4: 3 · (c) 6: 1 · (d) 4: 2
उत्तर और व्याख्या · explanation in English
Answer: (a) 6 : 5
A covers half the track, 180°. B started 30° ahead and is caught at that same point, so B covered 180° − 30° = 150° in the same time. The speeds are in the ratio 180 : 150 = 6 : 5.
- A runs from his start to the diametrically opposite point: an arc of 180°.
- B started 30° ahead in the direction of running and is met there: B runs 180° − 30° = 150°.
- Same time, so speed ratio = arc ratio = 180 : 150 = 6 : 5.
Remember · On a circular track, measure distances as angles; in equal time, the speed ratio equals the ratio of arcs covered.
Question and answer: UPSC's official GS Paper II (2018, Series A) — paper ↗ · answer key ↗. Explanation: Minimalist IAS, checked 30 Sept 2026 (how we verify). ·