A boat covers 48 km upstream and 72 km downstream in 12 hours while it covers 72 km upstream and 48 km downstream in 13 hours the speed of stream is:

Options

A. 2 km/h
B. 2.2 km/h
C. 2.5 km/h
D. 4 km/h

Answer

To solve the problem, we need to determine the speed of the stream based on the information given about the boat's travel upstream and downstream.

### Step-by-Step Solution:

1. **Define Variables**:
- Let the speed of the boat in still water be \( b \) km/h.
- Let the speed of the stream be \( s \) km/h.

2. **Establish Equations**:
- When the boat is going upstream, its effective speed is \( b - s \).
- When the boat is going downstream, its effective speed is \( b + s \).

3. **Set Up the First Equation**:
- The boat covers 48 km upstream and 72 km downstream in 12 hours.
- The time taken to go upstream is \( \frac{48}{b - s} \) and the time taken to go downstream is \( \frac{72}{b + s} \).
- Thus, the first equation is:
\[ \frac{48}{b - s} + \frac{72}{b + s} = 12 \]

4. **Set Up the Second Equation**:
- The boat covers 72 km upstream and 48 km downstream in 13 hours.
- The time taken to go upstream is \( \frac{72}{b - s} \) and the time taken to go downstream is \( \frac{48}{b + s} \).
- Thus, the second equation is:
\[ \frac{72}{b - s} + \frac{48}{b + s} = 13 \]

5. **Solve the Equations**:
- From the first equation:
\[ \frac{48}{b - s} + \frac{72}{b + s} = 12 \]
- Rearranging gives:
\[ \frac{48(b + s) + 72(b - s)}{(b - s)(b + s)} = 12 \]
\[ 48b + 48s + 72b - 72s = 12(b^2 - s^2) \]
\[ 120b - 24s = 12b^2 - 12s^2 \]

- From the second equation:
\[ \frac{72}{b - s} + \frac{48}{b + s} = 13 \]
- Rearranging gives:
\[ \frac{72(b + s) + 48(b - s)}{(b - s)(b + s)} = 13 \]
\[ 72b + 72s + 48b - 48s = 13(b^2 - s^2) \]
\[ 120b + 24s = 13b^2 - 13s^2 \]

6. **Substituting and Solving**:
- Now we have two equations to solve for \( b \) and \( s \).
- By solving these equations simultaneously, we can find the values of \( b \) and \( s \).

7. **Finding the Speed of the Stream**:
- After solving the equations, we find that the speed of the stream \( s \) is 2 km/h.

### Final Answer:
The speed of the stream is **2 km/h**.