Arvind and Chetan started running simultaneously from the same point in the same direction on a circular track of length 210 m. Arvind takes 180 seconds to complete one round, and Chetan takes 420 seconds to complete one round. After how much time will they meet for the first time at the starting point on the track?

Question

Accepted Answer

Arvind completes one round in 180 seconds, and Chetan completes one round in 420 seconds. They start together from the same point. We need to find the time after which both will meet again at the starting point simultaneously.

This is the problem of finding the Least Common Multiple (LCM) of their times to complete one round.

Step 1: Find LCM of 180 and 420.
- Prime factorization:
  180 = 2^2 * 3^2 * 5
  420 = 2^2 * 3 * 5 * 7

Step 2: LCM is the product of the highest powers of all prime factors:
- 2^2 (from both)
- 3^2 (from 180)
- 5 (from both)
- 7 (from 420)

LCM = 2^2 * 3^2 * 5 * 7 = 4 * 9 * 5 * 7 = 1260 seconds

Step 3: Convert 1260 seconds to minutes:
1260 ÷ 60 = 21 minutes

Therefore, they will meet for the first time at the starting point after 21 minutes.

However, the options given are 10, 15, 21, and 28 minutes. The correct answer is 21 minutes.

Answer

Answer

Answer