Ex 1.1 Q7 - 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 18 and 12.
*Let's find LCM of 18 and 12 by Prime factorization method,
18 = 2 × 3 × 3
12 = 2 × 2 × 3
∴ LCM of 18 and 12
= 2 × 2 × 3 × 3
= 36
Hence,
Sonia and Ravi will meet together after 36 minutes at the starting point.
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Try This..
✒ Find the LCM of 24 and 36 using prime factorization method.
✒ A and B start jogging around a circular track. A completes one round in 15 minutes, B in 10 minutes. After how many minutes will they meet at the starting point?
✒ Two bells ring at intervals of 20 and 25 minutes. If they ring together at 8:00 AM, when will they ring together next?
❌ Common Mistakes
Confusing LCM with HCF:▸ Remember, here we are looking for a time when both meet again, not the shortest possible time for one round. So use LCM, not HCF.Skipping prime factorization:▸ Directly guessing the LCM can lead to wrong answers. Always go step-by-step using factorization.Ignoring units:▸ Always keep your units in mind. Here, the answer is in minutes, not seconds or hours.
Queries Solved:-
Class 10 Ex 1.1
Ex 1.1 Q7 Class 10
Class 10 Ex 1.1 Q7
Class 10 Chap 1 Ex 1.1 Q7
Class 10 Real Numbers
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