There are two places X and Y, 200 km apart from each other. Initially two persons P and Q both are at 'X'. The speed of P is 20 km/h and speed of Q is 30 km/h. Later on they starts to move to and fro between X and Y.
If they starts to move between X and Y, then for the first time when they will meet each other?

Options

A. after 12 hours
B. after 24 hours
C. after 30 hours
D. after 8 hours

Answer

To solve the problem, we need to determine when two persons, P and Q, will meet for the first time while moving back and forth between two points, X and Y, which are 200 km apart.

### Step-by-Step Solution:

1. **Identify the speeds of P and Q**:
- Speed of P = 20 km/h
- Speed of Q = 30 km/h

2. **Calculate the relative speed**:
- Since both P and Q are moving towards each other, their relative speed is the sum of their speeds.
- Relative speed = Speed of P + Speed of Q = 20 km/h + 30 km/h = 50 km/h

3. **Determine the time taken to meet**:
- They will meet for the first time when the distance covered by both equals the total distance between X and Y (200 km).
- Time = Distance / Relative Speed
- Time = 200 km / 50 km/h = 4 hours

4. **Calculate the distance covered by each person**:
- Distance covered by P in 4 hours = Speed of P × Time = 20 km/h × 4 hours = 80 km
- Distance covered by Q in 4 hours = Speed of Q × Time = 30 km/h × 4 hours = 120 km

5. **Determine their positions when they meet**:
- Since P starts at X and moves towards Y, after 4 hours, P will be 80 km away from X (which means he is 120 km away from Y).
- Q, starting from X and moving towards Y, will have reached 120 km towards Y.

6. **Conclusion**:
- Therefore, P and Q will meet for the first time after 4 hours of travel.

### Final Answer:
P and Q will meet for the first time after **4 hours**.

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