Question

Ravi and Shikha drive around a circular sports field. Ravi takes 16 min to complete one round, while Shikha completes the round in 20 min. If both start at the same point, at same time and go in the same direction, then after how much time will they meet at the starting point?

Answer 1

Hint: Now we are given that Ravi takes 16 min to complete a drive around a circular sports field. Shikha also drives around the same circular sports field but to do so she takes 20 min. Hence they will meet at the time which is Lowest common multiple (LCM) of 16 and 20. Hence we just have to calculate the lowest common multiple (LCM) of 16 and 20.

Complete step by step answer:
Now we are given that Ravi drives around a circular sports field.
To drive around this circular sports field Ravi takes 16 min.
Also Shikha drives around the same circular sports field.
To drive around this sports field Shikha takes 20min.
Hence we know that they will meet after time which is Lowest common multiple (LCM) of 16 and 20.
Now let us first understand this. Ravi and Shikha start at the same point.
Ravi takes 16 minutes to complete one round of circular sports.
Hence after 16 minutes he will be at the starting point.
Now again after 16 minutes he will be at the starting point. Which means 16 + 16 = 32 minutes from the time he started.
Hence after every 16, 32, 48, 64, 80, 96… minutes Ravi will be at the starting point.
Now similarly if we check for Shikha she takes 20 min to complete one round.
Hence after every 20, 40, 60, 80, 100… minutes Shikha will be at the starting point.
Hence we can see that after 80 minutes they both will be at the starting point.
This is nothing but how the LCM is calculated which is the lowest common multiple of the given numbers since (LCM is the lowest common multiple of two numbers which means it is the first common multiple which arrives in both numbers)

Hence they both will meet at the starting point after 80 minutes.

Note: Not to be confused between LCM and HCF. LCM is the lowest common multiple of two numbers which means it is the first common multiple which arrives in both numbers. But HCF is the highest common factor which means out of all the common factors the two numbers have HCF is numerically the highest one. Note that to solve this question we will need LCM and not HCF.