A and B walk around a circular park. They start at 8 a.m. from the same point in the opposite directions. A and B walk at a speed of 2 rounds per hour and 3 rounds per hour respectively. How many times shall they cross each other after 8.00 a.m. and before 9.30. a.m.?
Answer & explanation
Answer: (a) 7
Walking in opposite directions they together cover 5 rounds an hour, so they meet every 12 minutes. In the 90 minutes up to 9:30 they cross at 12, 24, …, 84 minutes — 7 times.
- In opposite directions their speeds add: 2 + 3 = 5 rounds an hour.
- They meet each time they together complete one round: every 60 ÷ 5 = 12 minutes.
- 8:00 to 9:30 is 90 minutes: meetings at 12, 24, 36, 48, 60, 72 and 84 minutes.
- That is 7 crossings; the next would be at 96 minutes, after 9:30.
Remember · Opposite directions on a circular track: crossings = combined rounds covered, counting only whole rounds completed within the time.
Question and answer: UPSC's official GS Paper II (2016, Series A) — paper ↗ · answer key ↗. Explanation: Minimalist IAS, checked 30 Sept 2026 (how we verify). ·