Pawan can row 24 km/h in still water . When the river is running at 4.8 km/h,it takes him 1h to row to a place and to come back. How far is the place?

Options

A. 11.52 km
B. 14 km
C. 12.52 km
D. 15 km

Answer

To solve the problem, we need to determine the distance Pawan rows to a place in the river, given his rowing speed in still water and the speed of the river's current.

### Step-by-Step Solution:

1. **Identify Given Data:**
- Speed of Pawan in still water (V_p) = 24 km/h
- Speed of the river (V_r) = 4.8 km/h
- Total time taken for the round trip = 1 hour

2. **Calculate Effective Speeds:**
- When rowing downstream (with the current), the effective speed is:
\[ V_{down} = V_p + V_r = 24 + 4.8 = 28.8 \text{ km/h} \]
- When rowing upstream (against the current), the effective speed is:
\[ V_{up} = V_p - V_r = 24 - 4.8 = 19.2 \text{ km/h} \]

3. **Let the distance to the place be \( d \) km.**

4. **Set Up the Time Equation:**
- Time taken to row downstream to the place:
\[ t_{down} = \frac{d}{V_{down}} = \frac{d}{28.8} \]
- Time taken to row upstream back to the starting point:
\[ t_{up} = \frac{d}{V_{up}} = \frac{d}{19.2} \]
- According to the problem, the total time for the round trip is 1 hour:
\[ t_{down} + t_{up} = 1 \]
- Substitute the expressions for \( t_{down} \) and \( t_{up} \):
\[ \frac{d}{28.8} + \frac{d}{19.2} = 1 \]

5. **Finding a Common Denominator:**
- The common denominator of 28.8 and 19.2 is 57.6. Rewrite the equation:
\[ \frac{d \cdot 2}{57.6} + \frac{d \cdot 3}{57.6} = 1 \]
- Combine the fractions:
\[ \frac{5d}{57.6} = 1 \]

6. **Solve for \( d \):**
- Multiply both sides by 57.6:
\[ 5d = 57.6 \]
- Divide by 5:
\[ d = \frac{57.6}{5} = 11.52 \text{ km} \]

### Final Answer:
The distance to the place is **11.52 km**.