A man can row 20 kmph in still water. It takes him thrice as long to row up as to row down the river. Find the speed of the stream .

Options

A. 8 kmph
B. 10 kmph
C. 12 kmph
D. 15 kmph

Answer

To solve the problem, we need to find the speed of the stream when a man can row at a speed of 20 km/h in still water, and it takes him thrice as long to row upstream as it does to row downstream.

### Step-by-Step Solution:

1. **Define Variables:**
- Let the speed of the stream be \( v \) km/h.
- The speed of the man in still water is given as 20 km/h.

2. **Determine Speeds:**
- When rowing downstream (with the current), the effective speed of the man is:
\[ \text{Speed downstream} = 20 + v \text{ km/h} \]
- When rowing upstream (against the current), the effective speed of the man is:
\[ \text{Speed upstream} = 20 - v \text{ km/h} \]

3. **Set Up the Time Relationship:**
- Let the distance traveled be \( x \) km.
- The time taken to row downstream is:
\[ \text{Time downstream} = \frac{x}{20 + v} \]
- The time taken to row upstream is:
\[ \text{Time upstream} = \frac{x}{20 - v} \]
- According to the problem, the time taken to row upstream is three times the time taken to row downstream:
\[ \frac{x}{20 - v} = 3 \cdot \frac{x}{20 + v} \]

4. **Eliminate \( x \):**
- Since \( x \) is common in both terms, we can cancel it out (assuming \( x \neq 0 \)):
\[ \frac{1}{20 - v} = \frac{3}{20 + v} \]

5. **Cross-Multiply:**
- Cross-multiplying gives:
\[ 20 + v = 3(20 - v) \]
- Expanding the right side:
\[ 20 + v = 60 - 3v \]

6. **Combine Like Terms:**
- Rearranging the equation:
\[ v + 3v = 60 - 20 \]
\[ 4v = 40 \]

7. **Solve for \( v \):**
- Dividing both sides by 4:
\[ v = 10 \text{ km/h} \]

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