A fisherman rows a boat to a distance of 20 km. in 20 min. against the stream and returns in 15 min. Accordingly, what is the speed of stream ?

Options

A. 3 km./hr.
B. 4 km./hr.
C. 1 km./hr.
D. 2 km./hr.

Answer

To solve the problem, we need to find the speed of the stream based on the distances and times given for the fisherman rowing against and with the stream.

### Step-by-Step Solution:

1. **Convert Time to Hours**:
- The fisherman rows 20 km against the stream in 20 minutes.
- Convert 20 minutes to hours:
\[ \text{Time} = \frac{20}{60} = \frac{1}{3} \text{ hours} \]
- The fisherman rows 20 km downstream in 15 minutes.
- Convert 15 minutes to hours:
\[ \text{Time} = \frac{15}{60} = \frac{1}{4} \text{ hours} \]

2. **Calculate Speeds**:
- **Speed against the stream**:
\[ \text{Speed} = \frac{\text{Distance}}{\text{Time}} = \frac{20 \text{ km}}{\frac{1}{3} \text{ hours}} = 20 \times 3 = 60 \text{ km/h} \]
- **Speed with the stream**:
\[ \text{Speed} = \frac{\text{Distance}}{\text{Time}} = \frac{20 \text{ km}}{\frac{1}{4} \text{ hours}} = 20 \times 4 = 80 \text{ km/h} \]

3. **Set Up the Equation for Speed of the Stream**:
- Let \( v \) be the speed of the stream.
- The speed of the boat in still water is the average of the speeds against and with the stream:
\[ \text{Speed of boat} = \frac{60 + 80}{2} = 70 \text{ km/h} \]
- The speed against the stream is \( \text{Speed of boat} - v \) and the speed with the stream is \( \text{Speed of boat} + v \):
\[ 60 = 70 - v \quad \text{(1)} \]
\[ 80 = 70 + v \quad \text{(2)} \]

4. **Solve for \( v \)**:
- From equation (1):
\[ v = 70 - 60 = 10 \text{ km/h} \]
- From equation (2):
\[ v = 80 - 70 = 10 \text{ km/h} \]

5. **Conclusion**:
- The speed of the stream is \( 10 \text{ km/h} \).

### Final Answer:
The speed of the stream is **10 km/h**.