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?

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answer is A.

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Detailed Solution

Given,
Sonia takes time to drive one round = 18 minutes
Ravi takes time to drive one round = 12 minutes
The time for both meeting again = LCM of 18 and 12 in minutes
We find the LCM of 18 and 12 by Prime factorization
Now,
Factors of 18 and 12,
18 =

2 \times 3 \times 3

12 =

2 \times 2 \times 3

Greatest power of product of each prime factor.

= 2^{2} \times 3^{2}

= 4 \times 9

= 36

Thus, LCM (18, 12) = 36
Hence, after 36 minutes Sonia and Ravi meets again.
Correct option is 1.

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