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Four runners started running simultaneously from a point on a circular track. They took 200 seconds, 300 seconds, 360 seconds and 450 seconds to complete one round. After how much time they meet at the starting point for the first time? (SSC CGL 2nd Sit. 2011)
- a)1800 seconds
- b)3600 seconds
- c)2400 seconds
- d)4800 seconds
Correct answer is option 'A'. Can you explain this answer?
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Most Upvoted Answer
Four runners started running simultaneously from a point on a circular...
Understanding the Problem
To find out when the four runners meet at the starting point for the first time, we need to determine the least common multiple (LCM) of their individual times to complete one round.
Individual Rounding Times
- Runner 1: 200 seconds
- Runner 2: 300 seconds
- Runner 3: 360 seconds
- Runner 4: 450 seconds
Finding the LCM
To calculate the LCM, we can use the prime factorization method:
- **200 = 2^3 × 5^2**
- **300 = 2^2 × 3^1 × 5^2**
- **360 = 2^3 × 3^2 × 5^1**
- **450 = 2^1 × 3^2 × 5^2**
Now, to find the LCM, we take the highest power of each prime factor:
- **2: max(3, 2, 3, 1) = 3**
- **3: max(0, 1, 2, 2) = 2**
- **5: max(2, 2, 1, 2) = 2**
Thus, the LCM is:
- LCM = 2^3 × 3^2 × 5^2
Calculating the LCM
Calculating the values:
- **2^3 = 8**
- **3^2 = 9**
- **5^2 = 25**
Now, multiply them together:
- LCM = 8 × 9 × 25
First calculate:
- 8 × 9 = 72
- 72 × 25 = 1800
Conclusion
Thus, the first time all four runners meet at the starting point is after **1800 seconds**.
The correct answer is option **A) 1800 seconds**.
To find out when the four runners meet at the starting point for the first time, we need to determine the least common multiple (LCM) of their individual times to complete one round.
Individual Rounding Times
- Runner 1: 200 seconds
- Runner 2: 300 seconds
- Runner 3: 360 seconds
- Runner 4: 450 seconds
Finding the LCM
To calculate the LCM, we can use the prime factorization method:
- **200 = 2^3 × 5^2**
- **300 = 2^2 × 3^1 × 5^2**
- **360 = 2^3 × 3^2 × 5^1**
- **450 = 2^1 × 3^2 × 5^2**
Now, to find the LCM, we take the highest power of each prime factor:
- **2: max(3, 2, 3, 1) = 3**
- **3: max(0, 1, 2, 2) = 2**
- **5: max(2, 2, 1, 2) = 2**
Thus, the LCM is:
- LCM = 2^3 × 3^2 × 5^2
Calculating the LCM
Calculating the values:
- **2^3 = 8**
- **3^2 = 9**
- **5^2 = 25**
Now, multiply them together:
- LCM = 8 × 9 × 25
First calculate:
- 8 × 9 = 72
- 72 × 25 = 1800
Conclusion
Thus, the first time all four runners meet at the starting point is after **1800 seconds**.
The correct answer is option **A) 1800 seconds**.
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Community Answer
Four runners started running simultaneously from a point on a circular...
Required time = LCM of 200, 300, 360 and 450 seconds = 1800 seconds.
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Four runners started running simultaneously from a point on a circular track. They took 200 seconds, 300 seconds, 360 seconds and 450 seconds to complete one round. After how much time they meet at the starting point for the first time? (SSC CGL 2nd Sit. 2011)a)1800 secondsb)3600 secondsc)2400 secondsd)4800 secondsCorrect answer is option 'A'. Can you explain this answer?
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