A man rows upstrean 36 km and downstream 48 km taking 6 hours each time .The speed of the current is

Options

A. 0.5 kmph
B. 2 kmph
C. 1 kmph
D. 1.5 kmph

Answer

To solve the problem, we need to determine the speed of the current based on the information given about the man's rowing upstream and downstream.

### Step-by-Step Solution:

1. **Define Variables:**
Let's denote:
- \( x \) = speed of the man in still water (in km/h)
- \( y \) = speed of the current (in km/h)

2. **Set Up Equations:**
When rowing upstream, the effective speed is \( x - y \), and when rowing downstream, the effective speed is \( x + y \).

From the problem:
- The man rows 36 km upstream in 6 hours.
- The man rows 48 km downstream in 6 hours.

We can set up the following equations based on the formula:
\[ \text{Speed} = \frac{\text{Distance}}{\text{Time}} \]

For upstream:
\[ \frac{36}{6} = x - y \implies x - y = 6 \quad \text{(Equation 1)} \]

For downstream:
\[ \frac{48}{6} = x + y \implies x + y = 8 \quad \text{(Equation 2)} \]

3. **Solve the Equations:**
Now we have a system of two equations:
- \( x - y = 6 \) (Equation 1)
- \( x + y = 8 \) (Equation 2)

We can solve these equations by adding them together:
\[ (x - y) + (x + y) = 6 + 8 \]
This simplifies to:
\[ 2x = 14 \implies x = 7 \quad \text{(Speed of the man in still water)} \]

Now, substitute \( x = 7 \) back into either equation to find \( y \). We can use Equation 1:
\[ 7 - y = 6 \implies y = 1 \quad \text{(Speed of the current)} \]

4. **Conclusion:**
The speed of the current \( y \) is 1 km/h.

### Final Answer:
The speed of the current is **1 km/h**.