Four runners started running simultaneously from a point on a circular track They took 400 seconds 6...........

Quantitative Aptitude (CHSL) Time & distance

Four runners started running simultaneously from a point on a circular track. They took 400 seconds, 600 seconds, 720

seconds and 900 seconds to complete one round. After how much time did they meet at the starting point for the first time

since the race started?

This questions was previously asked in

SSC CHSL 3rd June 2022 Shift-1

4200 sec

2400 sec

3600 sec

1800 sec

- The task is to find the first time when all four runners meet at the starting point simultaneously.

- Since each runner completes the track in a different time, the first meeting occurs at the least common multiple (LCM) of their lap times.

- Runners' times to complete one round are: 400, 600, 720, and 900 seconds.

- Calculate LCM(400, 600, 720, 900):

- Break down into prime factors:

- 400 = 2^4 * 5^2

- 600 = 2^3 * 3 * 5^2

- 720 = 2^4 * 3^2 * 5

- 900 = 2^2 * 3^2 * 5^2

- LCM is found by taking the highest power of all prime numbers present:

- 2^4 (from 400 or 720)

- 3^2 (from 720 or 900)

- 5^2 (from 400, 600 or 900)

- Calculate LCM = 2^4 * 3^2 * 5^2 = 3600 seconds

- They will meet again 3600 seconds after starting.

- Option 3 - 3600 sec is therefore correct.

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