Question 7 of 10intermediate🔧 ApplyNumerical3 marks

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?

Correct Answer

Given: Time taken by Sonia for one round = 18 minutes Time taken by Ravi for one round = 12 minutes

Understanding: They will meet again at the starting point after a time that is a common multiple of both 18 and 12. We need to find the LCM of 18 and 12.

Prime Factorisation: 18 = 2×32 \times 3² 12 = 2² × 3

LCM(18, 12): LCM = 2² × 3² = 4×94 \times 9 = 36

Answer: They will meet again at the starting point after 36 minutes.

Verification: Sonia completes: 36 ÷ 18 = 2 rounds Ravi completes: 36 ÷ 12 = 3 rounds Both meet at the starting point after 36 minutes.

Exercise: Exercise 1.1 | Q: 7 | (Page Page 5-6)
For More Understanding

Explanation

This is an LCM problem. Sonia and Ravi will meet at the starting point when both have completed an integer number of rounds. This happens at a time that is a common multiple of their individual times. The first such time is the LCM of 18 and 12. Using prime factorisation: 18 = 2×32 \times 3² and 12 = 2² × 3, so LCM = 2² × 3² = 36 minutes.

Solution Steps

  1. Step 1: Identify that we need LCM of 18 and 12

  2. Step 2: Find prime factorisation: 18 = 2×32 \times 3², 12 = 2² × 3

  3. Step 3: LCM = Product of highest powers = 2² × 3² = 36

  4. Step 4: Verify: 36 ÷ 18 = 2 rounds for Sonia, 36 ÷ 12 = 3 rounds for Ravi

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