The speed of a train T is 100 km per hour and the speed of a person P is 4 km per hour. T crosses P in 15 seconds, if P travels along the direction of motion of T. If P travels along the opposite direction of T, then in how much time does T cross P, in seconds, approximately?
Answer & explanation
Answer: (c) 13.85
The train's length is fixed, so crossing time is inversely proportional to relative speed. Relative speed changes from 96 km/h to 104 km/h, so the new time is 15 × 96/104 ≈ 13·85 seconds.
- Same direction: relative speed = 100 − 4 = 96 km/h. Opposite direction: 100 + 4 = 104 km/h.
- Length of T = 96 × (5/18) m/s × 15 s = 400 m.
- Time in the opposite case = 400 ÷ (104 × 5/18) = 3600/260 ≈ 13·85 s.
- Check: 15 × 96/104 = 13·846 s.
Remember · Same length, different relative speed: new time = old time × old relative speed ÷ new relative speed.
Question and answer: UPSC's provisional GS Paper II (2026, Series A) — paper ↗ · answer key ↗. Explanation: Minimalist IAS, checked 30 Sept 2026 (how we verify). ·