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…

Quantitative Aptitude ·Previously asked in UPSC Civil Services Examination 2025

View the full solved paper: GS Paper II

Question

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?

  1. A. 15 m
  2. B. 18 m
  3. C. 20 m (Correct answer)
  4. D. 24 m

Correct Answer

Option C — 20 m

Detailed Solution & Explanation

The correct answer is 20 m.

Key Points

  • Let tram speed = v km/hr, length = L metres.
  • Relative speed vs X (3 km/hr): (v−3)×8/3600 = L/1000.
  • Relative speed vs Y (4 km/hr): (v−4)×9/3600 = L/1000.
  • So (v−3)×8 = (v−4)×9 → 8v−24 = 9v−36 → v=12 km/hr.
  • L = (12−3)×8×1000/3600 = 9×8/3.6 = 20 m. Answer: 20 m.