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)?
Answer & explanation
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). ·