A boatman goes 30 km along the stream in 2 hours and goes 15 km against the stream of stream in 5 hours. Find the speed of boatman in still water.

Options

A. 8 kmph
B. 9 kmph
C. 10 kmph
D. 11 kmph

Answer

To find the speed of the boatman in still water, we can use the information given about his travel along and against the stream.

### Step-by-Step Solution:

1. **Determine the Speed Along the Stream:**
- The boatman travels 30 km along the stream in 2 hours.
- Speed along the stream (S₁) = Distance / Time = 30 km / 2 hours = 15 km/h.

2. **Determine the Speed Against the Stream:**
- The boatman travels 15 km against the stream in 5 hours.
- Speed against the stream (S₂) = Distance / Time = 15 km / 5 hours = 3 km/h.

3. **Set Up the Equations:**
- Let B be the speed of the boat in still water and W be the speed of the stream.
- When going along the stream: B + W = S₁ = 15 km/h.
- When going against the stream: B - W = S₂ = 3 km/h.

4. **Create a System of Equations:**
- From the first equation: B + W = 15 (Equation 1)
- From the second equation: B - W = 3 (Equation 2)

5. **Solve the System of Equations:**
- Add Equation 1 and Equation 2:
- (B + W) + (B - W) = 15 + 3
- 2B = 18
- B = 18 / 2 = 9 km/h.

6. **Find the Speed of the Stream:**
- Substitute B back into either equation to find W:
- From Equation 1: 9 + W = 15
- W = 15 - 9 = 6 km/h.

### Final Answer:
The speed of the boatman in still water is **9 km/h**.