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CMA Foundation · Fundamentals of Business Mathematics and Statistics · Time and Distance

Two runners, Arjun and Bhavna, start together from the same point on a circular track 400 m long and run in the same direction. Arjun runs at 7 m/s and Bhavna at 5 m/s. After how many seconds will Arjun first overtake Bhavna (i.e., be one full lap ahead)?

Arjun first overtakes Bhavna after 200 seconds. Running in the same direction, their relative speed is 7 minus 5, which is 2 m/s, and he must gain a full 400 m lap. Time equals 400 divided by 2, giving 200 seconds.

  1. A100 seconds
  2. B200 secondsCorrect
  3. C133.33 seconds
  4. D400 seconds

Explanation

When running in the same direction, the relative speed is 7 - 5 = 2 m/s. Arjun must gain one full lap of 400 m, so time = 400/2 = 200 seconds. Using the sum of speeds (12 m/s) gives 33.33 s, which is the opposite-direction meeting time and is wrong here. Check: in 200 s Arjun runs 1400 m and Bhavna 1000 m, a difference of 400 m.

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