Two boats A and B start towards each other from two places , 108 km apart .Speed of the boa A and B in still water are 12 km /hr and 15 km /hr respectively . If A proceeds down and B up the stream , they will meet after .

Options

A. 4.5 hours
B. 4 hours
C. 5.4 hours
D. 6 hours

Answer

To solve the problem, we need to find out how long it will take for two boats, A and B, to meet when they are moving towards each other from a distance of 108 km apart. Boat A is moving downstream, and Boat B is moving upstream.

### Step-by-Step Solution:

1. **Identify the Speeds of the Boats**:
- Speed of Boat A in still water = 12 km/hr
- Speed of Boat B in still water = 15 km/hr

2. **Define the Speed of the Stream**:
- Let the speed of the stream be \( y \) km/hr.

3. **Calculate Downstream and Upstream Speeds**:
- Downstream speed of Boat A = Speed of Boat A + Speed of the stream = \( 12 + y \) km/hr
- Upstream speed of Boat B = Speed of Boat B - Speed of the stream = \( 15 - y \) km/hr

4. **Calculate the Relative Speed**:
- Since both boats are moving towards each other, their relative speed is the sum of their speeds:
\[ \text{Relative Speed} = (12 + y) + (15 - y) = 27 \text{ km/hr} \]

5. **Use the Distance to Find Time**:
- The distance between the two boats is 108 km. We can use the formula:
\[ \text{Time} = \frac{\text{Distance}}{\text{Relative Speed}} = \frac{108 \text{ km}}{27 \text{ km/hr}} = 4 \text{ hours} \]

6. **Conclusion**:
- Therefore, the two boats will meet after **4 hours**.

### Final Answer:
The two boats A and B will meet after **4 hours**.

---