A and B start walking along a circle from the same point, in opposite directions. They meet 30 m. from the starting point. While B has still not completed his circle, they meet again after having travelled at the same speed as before, at a distance of 50 m. from the starting point, but measured in the other direction as before. What is the circumference of the circle?

Options

A. 80 m
B. 110 m
C. 130 m
D. 160 m

Answer

To solve the problem step by step, let's break it down:

1. **Understanding the Problem**: A and B start walking from the same point on a circular path in opposite directions. They first meet 30 meters from the starting point, and then they meet again at a distance of 50 meters from the starting point, but in the opposite direction.

2. **First Meeting**:
- When A and B meet for the first time, B has traveled 30 meters.
- Let the distance A has traveled at this point be \( x \) meters.

3. **Second Meeting**:
- In the second meeting, A has traveled 50 meters from the starting point.
- Since they are walking in opposite directions, when A is at 50 meters, B has also traveled a certain distance.
- Since they meet again after traveling the same speed, we can conclude that B has traveled an additional 30 meters from the first meeting point.

4. **Calculating Distances**:
- From the first meeting to the second meeting, A travels from 30 meters to 50 meters, which is an additional 20 meters.
- B, who was at 30 meters, travels 30 meters to meet A again.
- Therefore, the distance B has traveled in total from the starting point when they meet the second time is \( 30 + 30 = 60 \) meters.

5. **Finding the Circumference**:
- The total distance traveled by A from the starting point to the second meeting is 50 meters.
- The total distance traveled by B from the starting point to the second meeting is 60 meters.
- The distance A has traveled when they first met is \( x = 30 + \text{(distance between the two meetings)} \).
- The total distance around the circle (circumference) can be found by adding the distances traveled by A and B until they meet again:
- Circumference = Distance A traveled + Distance B traveled = \( 50 + 60 = 110 \) meters.

6. **Conclusion**:
- The circumference of the circle is 110 meters.

### Final Answer:
The circumference of the circle is **110 meters**.