Multiple choice general knowledge math & puzzles

Arunanshu Pandey, Nitesh Ratre and Rahul Mittal are running on a circular track of length 300m. Pandey and Ratre are moving in the same direction while Mittal is moving in the opposite direction. Speed of Pandey,Ratre and Mittal are 4m/s,6m/s and 10m/s respectively. After how much time will all the three meet at the same point for the first time.

  1. 150 sec

  2. 150/8 sec

  3. 150/4 sec

  4. 150/2 sec
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A Correct answer
Explanation

Pandey and Mittal meet every 300/14 sec. Mittal and Ratre meet every 300/16 sec. For all three to meet simultaneously, we need LCM(300/14, 300/16) = 300*LCM(1/14, 1/16) = 300*(1/GCD(14,16)) = 300/2 = 150 sec. Verify: at 150 sec, Pandey at 600m (2 laps), Ratre at 900m (3 laps), Mittal at 1500m (5 laps), all at starting point.

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