A man can row upstream at 15 km/h and down stream at 21 km/h the speed of water current of the river is:

Options

A. 8 km/h
B. 6 km/h
C. 3 km/h
D. 5 km/h

Answer

To find the speed of the water current in the river, we can use the information given about the rowing speeds upstream and downstream.

### Step-by-Step Solution:

1. **Understand the Terms**:
- Let \( B \) be the speed of the man in still water (boat speed).
- Let \( W \) be the speed of the water current.
- When rowing upstream, the effective speed is \( B - W \).
- When rowing downstream, the effective speed is \( B + W \).

2. **Set Up the Equations**:
- From the problem, we know:
- Upstream speed: \( B - W = 15 \) km/h
- Downstream speed: \( B + W = 21 \) km/h

3. **Add the Two Equations**:
- Adding the two equations:
\[ (B - W) + (B + W) = 15 + 21 \]
This simplifies to:
\[ 2B = 36 \]
Therefore:
\[ B = \frac{36}{2} = 18 \text{ km/h} \]

4. **Substitute Back to Find \( W \)**:
- Now, substitute \( B \) back into one of the original equations to find \( W \). Using the downstream equation:
\[ B + W = 21 \]
Substitute \( B = 18 \):
\[ 18 + W = 21 \]
Solving for \( W \):
\[ W = 21 - 18 = 3 \text{ km/h} \]

5. **Conclusion**:
- The speed of the water current \( W \) is 3 km/h.

### Final Answer:
The speed of the water current of the river is **3 km/h**.