A man can row downstream at 12 km/h and upstream at 8 kn/h what is the speed of man in still water?

Options

A. 12 km/h
B. 10 km/h
C. 8 km/h
D. 9 km/h

Answer

To find the speed of the man in still water, we can use the information provided about his rowing speeds downstream and upstream.

### Step-by-Step Solution:

1. **Define Variables**:
- Let \( B \) be the speed of the man in still water (in km/h).
- Let \( W \) be the speed of the water current (in km/h).

2. **Set Up Equations**:
- The speed downstream (with the current) is given by:
\[ B + W = 12 \quad \text{(1)} \]
- The speed upstream (against the current) is given by:
\[ B - W = 8 \quad \text{(2)} \]

3. **Add the Two Equations**:
- Adding equations (1) and (2):
\[ (B + W) + (B - W) = 12 + 8 \]
- This simplifies to:
\[ 2B = 20 \]

4. **Solve for \( B \)**:
- Divide both sides by 2:
\[ B = \frac{20}{2} = 10 \]

5. **Conclusion**:
- The speed of the man in still water is \( 10 \) km/h.

### Final Answer:
The speed of the man in still water is **10 km/h**.