A man can row 32 km in 4 hours along the stream and cover the same distance in 8 hours against the water. Find the speed of stream.

Options

A. 2 kmph
B. 3 kmph
C. 4 kmph
D. 5 kmph

Answer

To solve the problem, we need to find the speed of the stream (W) given the rowing speeds of a man along the stream and against the stream.

### Step-by-Step Solution:

1. **Identify the Given Information:**
- Distance (D) = 32 km
- Time taken to row along the stream (T1) = 4 hours
- Time taken to row against the stream (T2) = 8 hours

2. **Calculate the Speed Along the Stream:**
- Speed along the stream (B + W) can be calculated using the formula:
\[ \text{Speed} = \frac{\text{Distance}}{\text{Time}} \]
- Therefore, the speed along the stream is:
\[ B + W = \frac{32 \text{ km}}{4 \text{ hours}} = 8 \text{ km/h} \]

3. **Calculate the Speed Against the Stream:**
- Speed against the stream (B - W) can also be calculated using the same formula:
- Therefore, the speed against the stream is:
\[ B - W = \frac{32 \text{ km}}{8 \text{ hours}} = 4 \text{ km/h} \]

4. **Set Up the Equations:**
- We now have two equations:
1. \( B + W = 8 \) (Equation 1)
2. \( B - W = 4 \) (Equation 2)

5. **Solve the Equations:**
- To find the speed of the stream (W), we can add both equations:
\[ (B + W) + (B - W) = 8 + 4 \]
This simplifies to:
\[ 2B = 12 \implies B = 6 \text{ km/h} \]
- Now, substitute \( B \) back into one of the equations to find \( W \):
- Using Equation 1:
\[ 6 + W = 8 \implies W = 8 - 6 = 2 \text{ km/h} \]

6. **Conclusion:**
- The speed of the stream (W) is 2 km/h.