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A, B and C start at the same time in the same direction to run around a circular stadium. A completes a round in 252 seconds, B in 308 seconds and C in 198 seconds, all starting at the same point. After what time will they meet again at the starting point?
- a)15 minutes 15 seconds
- b)42 minutes 30 seconds
- c)42 minutes
- d)46 minutes 12 seconds
- e)None of these
Correct answer is option 'D'. Can you explain this answer?
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Verified Answer
A, B and C start at the same time in the same direction to run around ...
L.C.M. of 252, 308 and 198 = 2772.So, A, B and C will again meet at the starting point in 2772 see i.e., 46 min. 12 sec
Most Upvoted Answer
A, B and C start at the same time in the same direction to run around ...
Problem Analysis:
To solve this problem, we need to find the time at which A, B, and C will meet again at the starting point. Since they all start at the same time and in the same direction, they will meet again when the relative distance covered by each person is a multiple of the circumference of the circular stadium.
Solution:
Let's calculate the time at which they will meet again.
Step 1: Find the time taken by each person to cover the distance of one round.
- A completes a round in 252 seconds.
- B completes a round in 308 seconds.
- C completes a round in 198 seconds.
Step 2: Find the least common multiple (LCM) of the time taken by each person.
The LCM of 252, 308, and 198 can be found by prime factorization as follows:
- Prime factorization of 252: 2^2 * 3^2 * 7
- Prime factorization of 308: 2^2 * 7 * 11
- Prime factorization of 198: 2 * 3^2 * 11
To calculate the LCM, we take the highest power of each prime factor that appears in the prime factorizations:
- LCM = 2^2 * 3^2 * 7 * 11 = 2772 seconds
Step 3: Convert the LCM to minutes and seconds.
Since 60 seconds make 1 minute, we can divide the LCM by 60 to get the time in minutes and seconds.
2772 seconds ÷ 60 = 46 minutes and 12 seconds
Therefore, A, B, and C will meet again at the starting point after 46 minutes and 12 seconds.
Answer:
The correct answer is option D) 46 minutes and 12 seconds.
To solve this problem, we need to find the time at which A, B, and C will meet again at the starting point. Since they all start at the same time and in the same direction, they will meet again when the relative distance covered by each person is a multiple of the circumference of the circular stadium.
Solution:
Let's calculate the time at which they will meet again.
Step 1: Find the time taken by each person to cover the distance of one round.
- A completes a round in 252 seconds.
- B completes a round in 308 seconds.
- C completes a round in 198 seconds.
Step 2: Find the least common multiple (LCM) of the time taken by each person.
The LCM of 252, 308, and 198 can be found by prime factorization as follows:
- Prime factorization of 252: 2^2 * 3^2 * 7
- Prime factorization of 308: 2^2 * 7 * 11
- Prime factorization of 198: 2 * 3^2 * 11
To calculate the LCM, we take the highest power of each prime factor that appears in the prime factorizations:
- LCM = 2^2 * 3^2 * 7 * 11 = 2772 seconds
Step 3: Convert the LCM to minutes and seconds.
Since 60 seconds make 1 minute, we can divide the LCM by 60 to get the time in minutes and seconds.
2772 seconds ÷ 60 = 46 minutes and 12 seconds
Therefore, A, B, and C will meet again at the starting point after 46 minutes and 12 seconds.
Answer:
The correct answer is option D) 46 minutes and 12 seconds.
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