Two men start walking from same point at same time in same direction to take a round of circular route. If one take 10 min and second take 15 min complete the round, at what time will they meet each other ?

Options

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

Answer

To solve the problem, we need to determine when the two men will meet again after starting from the same point and walking in the same direction around a circular route.

### Step-by-Step Solution:

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

2. **Determine the speeds of each man:**
- Since speed is inversely proportional to time taken for a fixed distance (the circular route), we can express their speeds:
- Speed of Man A = 1 round / 10 minutes = 1/10 rounds per minute
- Speed of Man B = 1 round / 15 minutes = 1/15 rounds per minute

3. **Calculate the relative speed:**
- Since both men are moving in the same direction, the relative speed is the difference in their speeds:
- Relative speed = Speed of Man A - Speed of Man B
- Relative speed = (1/10 - 1/15) rounds per minute

4. **Find a common denominator to subtract the speeds:**
- The least common multiple (LCM) of 10 and 15 is 30.
- Convert the speeds:
- Speed of Man A = 3/30 rounds per minute
- Speed of Man B = 2/30 rounds per minute
- Now, calculate the relative speed:
- Relative speed = (3/30 - 2/30) = 1/30 rounds per minute

5. **Determine the time taken to meet:**
- To find out when they will meet, we need to find out how long it takes for the faster man to gain one complete round over the slower man.
- Time = 1 round / Relative speed
- Time = 1 / (1/30) = 30 minutes

### Conclusion:
The two men will meet each other again after **30 minutes**.