UPSC Prelims 2016·CSAT·Quantitative Aptitude·Time, Speed and Distance

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.?

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Last updated 23 May 2026, 3:31 pm IST
  1. A7Correct
  2. B6
  3. C5
  4. D8

Explanation

To solve this problem, we look at the relative speed of A and B. When two people move in opposite directions around a circular track, their relative speed is the sum of their individual speeds. A walks at 2 rounds per hour and B walks at 3 rounds per hour. Therefore, their relative speed is 2 plus 3, which equals 5 rounds per hour. This means they will cross each other 5 times every hour. The time duration from 8.00 a.m. to 9.30 a.m. is 1.5 hours. To find the total number of crossings, multiply the relative speed by the total time: 5 rounds per hour multiplied by 1.5 hours equals 7.5. Since they can only cross each other a whole number of times, they will cross 7 times before 9.30 a.m. The 8th crossing would occur at the 1.6 hour mark, which is after 9.30 a.m. Therefore, the correct answer is 7.
Quantitative Aptitude: 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 a
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