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 a…

Quantitative Aptitude ·Previously asked in UPSC Civil Services Examination 2026

View the full solved paper: GS Paper II

Question

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?

  1. A. 13.51
  2. B. 13.65
  3. C. 13.85 (Correct answer)
  4. D. 14.05

Correct Answer

Option C — 13.85

Detailed Solution & Explanation

The correct answer is Option C (≈13.85 seconds).

Key Points

  • Same direction: relative speed = 100 − 4 = 96 km/h. Crossing in 15 s gives train length = 96 × (15/3600) = 0.4 km.
  • Opposite direction: relative speed = 100 + 4 = 104 km/h. Time = 0.4 / 104 × 3600 = 1440/104 ≈ 13.85 s.

Additional Information

  • The train length is fixed; only the relative speed changes, giving Option C.