Question

Ramesh takes 18 minutes to complete a round of a ground which Aslam takes 24 minutes to complete the same round. Suppose they start from the same point and at the same time and go in the same direction. After how many minutes will they meet again? How many times will they meet in 6 hours?

Answer 1

It can be observed that Ramesh takes lesser time than Aslam for completing 1 round of the circular path. As they are going in the same direction, they will meet again at the same time when Ramesh will have completed 1 round of that circular path with respect to Aslam. And the total time taken for completing this 1 round of circular path will be the LCM of time taken by Aslam and Ramesh for completing 1 round of circular path respectively i.e., LCM of 24 minutes and 18 minutes.

24 = 2 × 2 × 2 ×3

And, 18 = 2 × 3 × 3

LCM of 24 and 18 = 2 × 2 × 2 × 3 × 3 = 72

Therefore, Ramesh and Aslam will meet together at the starting point after 72 minutes.

6 hour = 6 × 60
= 360 minutes.

Ramesh and Aslam meets at 72, 144, 216, 288, and 360 minutes.

Therefore,
They meet 5 times with in 6 hour.