A man moves 20 km down stream in 5 hours and 10 km up stream in same time. The speed of stream

Options

A. 4 km/h
B. 1 km/h
C. 1.6 km/h
D. None

Answer

To solve the problem, we need to find the speed of the stream based on the information provided about the man's movement downstream and upstream.

### Step-by-Step Solution:

1. **Define Variables:**
- Let \( x \) be the speed of the man in still water (in km/h).
- Let \( y \) be the speed of the stream (in km/h).

2. **Determine Downstream and Upstream Speeds:**
- When moving downstream, the effective speed is \( x + y \).
- When moving upstream, the effective speed is \( x - y \).

3. **Use the Given Information:**
- The man moves 20 km downstream in 5 hours.
- The man moves 10 km upstream in the same 5 hours.

4. **Set Up Equations:**
- For downstream:
\[ \text{Distance} = \text{Speed} \times \text{Time} \]
\[ 20 = (x + y) \times 5 \]
Dividing both sides by 5:
\[ x + y = 4 \quad \text{(Equation 1)} \]

- For upstream:
\[ 10 = (x - y) \times 5 \]
Dividing both sides by 5:
\[ x - y = 2 \quad \text{(Equation 2)} \]

5. **Solve the Equations:**
- Now we have two equations:
1. \( x + y = 4 \)
2. \( x - y = 2 \)

- Add both equations to eliminate \( y \):
\[ (x + y) + (x - y) = 4 + 2 \]
\[ 2x = 6 \]
\[ x = 3 \]

- Substitute \( x \) back into Equation 1 to find \( y \):
\[ 3 + y = 4 \]
\[ y = 4 - 3 \]
\[ y = 1 \]

6. **Conclusion:**
- The speed of the stream \( y \) is **1 km/h**.