A tram overtakes 2 persons X and Y walking at an average speed of 3 km/hr and 4 km/hr in the same direction and completely passes them in 8 seconds and 9 seconds respectively. What is the length of the tram?
Answer & explanation
Answer: (c) 20 m
To pass a walker, the tram covers its own length at the relative speed, so (v − 3) × 8 = (v − 4) × 9, giving v = 12 km/h. Relative to X it moves at 9 km/h = 2.5 m/s, so in 8 seconds it covers 20 m, which is its length.
- Let the tram's speed be v km/h. Passing a walker completely means covering the tram's length at the relative speed.
- Length = (v − 3) × 8 = (v − 4) × 9 (same units), so 8v − 24 = 9v − 36 and v = 12 km/h.
- Relative speed past X = 12 − 3 = 9 km/h = 9 × 5/18 = 2.5 m/s.
- Length = 2.5 m/s × 8 s = 20 m.
- Check with Y: (12 − 4) × 5/18 = 20/9 m/s, and 20/9 × 9 s = 20 m.
Remember · Overtaking a moving person: length = speed difference × time; equate two such lengths to find the speed. 1 km/h = 5/18 m/s.
Question and answer: UPSC's official GS Paper II (2025, Series A) — paper ↗ · answer key ↗. Explanation: Minimalist IAS, checked 30 Sept 2026 (how we verify). ·