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. ?
- (a) 7 ✓ UPSC's answer
- (b) 6
- (c) 5
- (d) 8
Why the answer is (a)
• A and B walk in opposite directions, so their relative speed is the sum of their individual speeds: 2 + 3 = 5 rounds per hour.
• They meet every time their combined distance covered equals one full round of the park.
• The time interval between consecutive meetings is 1 / 5 hour, which equals 12 minutes.
• The total time duration from 8:00 a.m. to 9:30 a.m. is 1.5 hours, or 90 minutes.
• The number of meetings is calculated by dividing the total time by the interval between meetings: 90 minutes / 12 minutes = 7.5.
• Since they cannot meet half a time, we count only the complete meetings that occur strictly before 9:30 a.m., which is 7 times (at 12, 24, 36, 48, 60, 72, and 84 minutes after 8:00 a.m.).
Why the other options are wrong
- (b) 6
- Option 6 is incorrect because it undercounts the meetings; there are actually 7 full meetings within the 90-minute window.
- (c) 5
- Option 5 is incorrect because it significantly undercounts the frequency of meetings based on the relative speed of 5 rounds per hour.
- (d) 8
- Option 8 is incorrect because the 8th meeting would occur at 96 minutes (1 hour 36 minutes) after 8:00 a.m., which is after 9:30 a.m.
Asked in the CSAT Paper II of the UPSC Civil Services Preliminary Examination 2016, held on 7 August 2016. Question and answer key: Union Public Service Commission. Explanation: UPSC Answer Check.