A boy from Delhi and a girl from Meerut started walking towards each other. They both started withthe speed of 5 km/h. After every 1 hour the boy increased his speed by 1 km/h and the girl decreased her speed by 1 km/h. Distance between Delhi & Meerut is 110 km. Find the time taken by them to meet each other.

Answer

To solve the problem step by step, we need to analyze the situation of the boy and the girl walking towards each other, taking into account their changing speeds.

### Step-by-Step Solution:

1. **Initial Speeds**:
- The boy's initial speed = 5 km/h
- The girl's initial speed = 5 km/h

2. **Distance Between Them**:
- The total distance between Delhi and Meerut = 110 km

3. **Speed Changes**:
- After every hour, the boy increases his speed by 1 km/h and the girl decreases her speed by 1 km/h.

4. **Distance Covered in the First Hour**:
- Combined speed in the first hour = Boy's speed + Girl's speed = 5 km/h + 5 km/h = 10 km/h
- Distance covered in the first hour = 10 km

5. **Remaining Distance After First Hour**:
- Remaining distance = Total distance - Distance covered in the first hour = 110 km - 10 km = 100 km

6. **Speeds After the First Hour**:
- Boy's speed after 1 hour = 5 km/h + 1 km/h = 6 km/h
- Girl's speed after 1 hour = 5 km/h - 1 km/h = 4 km/h
- Combined speed after the first hour = 6 km/h + 4 km/h = 10 km/h

7. **Distance Covered in the Second Hour**:
- Distance covered in the second hour = Combined speed × Time = 10 km/h × 1 hour = 10 km
- Remaining distance = 100 km - 10 km = 90 km

8. **Speeds After the Second Hour**:
- Boy's speed after 2 hours = 6 km/h + 1 km/h = 7 km/h
- Girl's speed after 2 hours = 4 km/h - 1 km/h = 3 km/h
- Combined speed after the second hour = 7 km/h + 3 km/h = 10 km/h

9. **Distance Covered in the Third Hour**:
- Distance covered in the third hour = 10 km
- Remaining distance = 90 km - 10 km = 80 km

10. **Repeating the Process**:
- This pattern continues, where every hour they cover 10 km together until the distance is covered.

11. **Calculating Total Time**:
- Since they cover 10 km every hour, we can find the total time taken to cover the remaining distance of 110 km.
- Total distance = 110 km
- Distance covered every hour = 10 km
- Total time taken = Total distance / Distance covered per hour = 110 km / 10 km/h = 11 hours

### Final Answer:
The time taken by the boy and the girl to meet each other is **11 hours**.