Speed of a boat is 4 km per hour in still water and the speed of the stream is 2 km per hour. If the boat takes 8 hours to go to a place and come back, then what is the distance of the place?

Options

A. 12
B. 9
C. 15
D. 18

Answer

To solve the problem, we need to determine the distance to the place based on the given speeds of the boat and the stream, as well as the total time taken for the round trip.

### Step-by-Step Solution:

1. **Identify the Speeds**:
- Speed of the boat in still water = 4 km/h
- Speed of the stream = 2 km/h

2. **Calculate Effective Speeds**:
- When going downstream (with the stream), the effective speed of the boat = Speed of the boat + Speed of the stream = 4 km/h + 2 km/h = 6 km/h
- When going upstream (against the stream), the effective speed of the boat = Speed of the boat - Speed of the stream = 4 km/h - 2 km/h = 2 km/h

3. **Let the Distance to the Place be 'd' km**:
- Time taken to go downstream = Distance / Speed = d / 6 hours
- Time taken to come back upstream = Distance / Speed = d / 2 hours

4. **Total Time for the Round Trip**:
- Total time taken for the trip = Time downstream + Time upstream
- According to the problem, this total time is 8 hours:
\[ \frac{d}{6} + \frac{d}{2} = 8 \]

5. **Finding a Common Denominator**:
- The common denominator for 6 and 2 is 6. Rewrite the equation:
\[ \frac{d}{6} + \frac{3d}{6} = 8 \]
- This simplifies to:
\[ \frac{4d}{6} = 8 \]

6. **Simplify the Equation**:
- Multiply both sides by 6 to eliminate the fraction:
\[ 4d = 48 \]

7. **Solve for 'd'**:
- Divide both sides by 4:
\[ d = 12 \]

### Conclusion:
The distance to the place is **12 km**.