# There is a circular path around a sports field. Sonia takes 18 minutes to drive one round of the field, while Ravi takes 12 minutes for the same. Suppose they both start at the same point and at the same time and go in the same direction. After how many minutes will they meet again at the starting point?

**Solution:**

Given:

- Sonia takes 18 minutes to drive one round of the field.
- Ravi takes 12 minutes for the same.
- They both start at the same point and at the same time and go in the same direction.

Time taken by Sonia is more than Ravi to complete one round. Now, we have to find after how many minutes will they meet again at the same point. For this, there will be a number that is divisible by both 18 and 12, and that will be the time when both meet again at the starting point. To find this we have to take LCM of both numbers.

Let's find LCM of 18 and 12 by prime factorization method.

18 = 2 × 3 × 3

12 = 2 × 2 × 3

LCM of 12 and 18 = 2 × 2 × 3 × 3 = 36

Therefore, Ravi and Sonia will meet together at the starting point after 36 minutes.

**☛ Check: **NCERT Solutions Class 10 Maths Chapter 1

**Video Solution:**

## There is a circular path around a sports field. Sonia takes 18 minutes to drive one round of the field, while Ravi takes 12 minutes for the same. Suppose they both start at the same point and at the same time and go in the same direction. After how many minutes will they meet again at the starting point?

NCERT Solutions Class 10 Maths Chapter 1 Exercise 1.2 Question 7

**Summary:**

There is a circular path around a sports field. Sonia takes 18 minutes to drive one round of the field, while Ravi takes 12 minutes for the same. Suppose they both start at the same point and at the same time and go in the same direction, they will meet again at the starting point after 36 minutes.

**☛ Related Questions:**

- Find the LCM and HCF of the following integers by applying the prime factorisation method. (i) 12, 15 and 21 (ii) 17, 23 and 29 (iii) 8, 9 and 25
- Given that HCF (306, 657) = 9, find LCM (306, 657).
- Check whether 6n can end with the digit 0 for any natural number n.
- Explain why 7 × 11 × 13 + 13 and 7 × 6 × 5 × 4 × 3 × 2 × 1 + 5 are composite numbers.

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