P and Q walk along a circular track. They start at 5:00 a.m. from the same point in opposite directions. P walks at an average sp…

Quantitative Aptitude ·Previously asked in UPSC Civil Services Examination 2025

View the full solved paper: GS Paper II

Question

P and Q walk along a circular track. They start at 5:00 a.m. from the same point in opposite directions. P walks at an average speed of 5 rounds per hour and Q walks at an average speed of 3 rounds per hour. How many times will they cross each other between 5:20 a.m. and 7:00 a.m.?

  1. A. 12
  2. B. 13 (Correct answer)
  3. C. 14
  4. D. 11

Correct Answer

Option B — 13

Detailed Solution & Explanation

The correct answer is 13.

Key Points

  • P and Q move in opposite directions at 5+3=8 rounds/hour combined.
  • They cross every 1/8 hour = 7.5 minutes.
  • From 5:00 to 5:20 = 20 minutes: crosses at 7.5, 15 min = 2 crosses.
  • From 5:20 to 7:00 = 100 minutes.
  • In 100 min at 1 cross/7.5 min = 13.33 → 13 crosses.
  • Total between 5:20 and 7:00 = 13. Answer: 13.