Two men start together from the some place in the same direction to go round a circular path. If one takes 10 minutes and the other takes 15 minutes to make one complete round they will meet after

Options

A. 30 minutes
B. 33 minutes
C. 40 minutes
D. 45 minutes

Answer

To solve the problem of when two men will meet while running around a circular path, we can follow these steps:

### Step 1: Identify the time taken by each man to complete one round.
- Man A takes 10 minutes to complete one round.
- Man B takes 15 minutes to complete one round.

### Step 2: Determine the time interval at which they will meet.
To find out when they will meet again after starting together, we need to find the least common multiple (LCM) of the two times (10 minutes and 15 minutes).

### Step 3: Calculate the LCM of 10 and 15.
- The prime factorization of 10 is \(2 \times 5\).
- The prime factorization of 15 is \(3 \times 5\).
- The LCM is found by taking the highest power of each prime factor:
- For 2: highest power is \(2^1\)
- For 3: highest power is \(3^1\)
- For 5: highest power is \(5^1\)

Thus, the LCM is:
\[ LCM = 2^1 \times 3^1 \times 5^1 = 30 \]

### Step 4: Conclusion
The two men will meet after 30 minutes.

### Final Answer
They will meet after **30 minutes**.

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