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 ?
- (a) 15 m
- (b) 18 m
- (c) 20 m ✓ UPSC's answer
- (d) 24 m
Why the answer is (c)
• Let the tram's speed be v km/h. All three move in the same direction, so the tram gains on X at (v − 3) km/h and on Y at (v − 4) km/h.
• To pass a walker completely the tram covers its own length L, so L = relative speed × time (with km/h × 5/18 giving m/s).
• For X: L = (v − 3) × 5/18 × 8. For Y: L = (v − 4) × 5/18 × 9.
• Equating: 8(v − 3) = 9(v − 4), so 8v − 24 = 9v − 36 and v = 12 km/h.
• Then L = (12 − 3) × 5/18 × 8 = 9 × 5/18 × 8 = 20 m, option (c).
Why the other options are wrong
- (a) 15 m
- With L = 15 m the tram would pass X at 15/8 m/s (6.75 km/h), so v = 9.75 km/h; it would then take about 9.4 s, not 9 s, to pass Y.
- (b) 18 m
- With L = 18 m the tram would pass X at 18/8 m/s (8.1 km/h), so v = 11.1 km/h; it would then take about 9.1 s, not 9 s, to pass Y.
- (d) 24 m
- With L = 24 m the tram would pass X at 24/8 m/s (10.8 km/h), so v = 13.8 km/h; it would then take about 8.8 s, not 9 s, to pass Y.
Asked in the CSAT Paper II of the UPSC Civil Services Preliminary Examination 2025, held on 25 May 2025. Question and answer key: Union Public Service Commission. Explanation: UPSC Answer Check.