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A, B and C starting running simultaneously on a circular track of length 2400 metres at speeds of 8m/s, 10 m/s and 12 m/s in the same direction. What is the minimum time after which they meet at the starting point?
  • a)
    10 minutes
  • b)
    15 minutes
  • c)
    20 minutes
  • d)
    24 minutes
Correct answer is option 'C'. Can you explain this answer?
Most Upvoted Answer
A, B and C starting running simultaneously on a circular track of len...
A, B and C complete one circle in 300 s, 240 s and 200 s respectively.
So, the minimum time when they meet at the starting point is LCM (200,240,300) = 1200 secs = 20 minutes
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Community Answer
A, B and C starting running simultaneously on a circular track of len...
To find the minimum time after which A, B, and C meet at the starting point on a circular track, we need to find the time it takes for all three runners to cover the same distance.

Let's find the time it takes for each runner individually.

Runner A:
Speed of A = 8 m/s
Distance to cover = 2400 m
Time taken by A = Distance / Speed = 2400 / 8 = 300 seconds = 5 minutes

Runner B:
Speed of B = 10 m/s
Distance to cover = 2400 m
Time taken by B = Distance / Speed = 2400 / 10 = 240 seconds = 4 minutes

Runner C:
Speed of C = 12 m/s
Distance to cover = 2400 m
Time taken by C = Distance / Speed = 2400 / 12 = 200 seconds = 3 minutes 20 seconds

To find the minimum time after which they meet at the starting point, we need to find the least common multiple (LCM) of the individual times taken by A, B, and C.

LCM(5 minutes, 4 minutes, 3 minutes 20 seconds) = LCM(5, 4, 3.33)

To simplify the calculation, let's convert all the values into seconds.

LCM(300 seconds, 240 seconds, 200 seconds) = LCM(300, 240, 200)

Now, let's find the LCM.

LCM(300, 240, 200) = 1200 seconds = 20 minutes

Therefore, the minimum time after which they meet at the starting point is 20 minutes.

Hence, the correct answer is option C) 20 minutes.
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