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?

(a) 13·51
(b) 13·65
(c) 13·85 ✓ UPSC's answer
(d) 14·05

Why the answer is (c)

• Same direction: relative speed = 100 − 4 = 96 km/h. In 15 s the train covers its own length: L = 96 × 15/3600 = 0·4 km.

• Opposite direction: relative speed = 100 + 4 = 104 km/h.

• Time = 0·4/104 h = 0·4 × 3600/104 s ≈ 13·85 s: (c).

Why the other options are wrong

(a) 13·51: 13·51 s does not follow from a 0·4 km train at 104 km/h.
(b) 13·65: 13·65 s is too short; 1440/104 ≈ 13·85 s.
(d) 14·05: 14·05 s is too long; 1440/104 ≈ 13·85 s.

Asked in the CSAT Paper II of the UPSC Civil Services Preliminary Examination 2026, held on 24 May 2026. Question and answer key: Union Public Service Commission. Explanation: UPSC Answer Check.