‘A’ walks around a circular field at the rate of one round per hour while ‘B’ runs around it at the rate of six rounds per hour. They start in the same direction from the same point at 7.30 a.m. They shall first cross each other at
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UPSC Civil Services preparation
- A8.30 a.m.
- B8.10 a.m.
- C7.48 a.m.
- D7.42 a.m.Correct
Explanation
To solve this, we use the concept of relative speed in a circular track.
1. Speed of A is 1 round per hour.
2. Speed of B is 6 rounds per hour.
3. Since they are moving in the same direction, their relative speed is the difference between their speeds. Relative speed = 6 minus 1 = 5 rounds per hour.
4. They will cross each other for the first time when the faster person B covers a relative distance of exactly 1 round over person A.
5. Time taken to cross = Distance / Relative Speed = 1 / 5 hours.
6. To convert this into minutes: 1 / 5 multiplied by 60 minutes = 12 minutes.
7. They started at 7.30 a.m. Adding 12 minutes to the starting time, they will first cross each other at 7.42 a.m.
Therefore, option D is correct.
