In a river, the ratio of the speed of stream and speed of a boat in still water is 2:5. Again, ratio of the speed of stream and speed of an another boat in still water is 3:4 What is the ratio of the speeds of the first boat to the second boat in still water?

Options

A. `10:7`
B. `15:8`
C. `4:3`
D. `5:4`

Answer

To solve the problem, we need to find the ratio of the speeds of the first boat to the second boat in still water based on the given ratios of the speed of the stream to the speed of each boat.

### Step-by-Step Solution:

1. **Define Variables**:
- Let the speed of the stream be \( y \) km/h.
- Let the speed of the first boat in still water be \( x \) km/h.
- Let the speed of the second boat in still water be \( p \) km/h.

2. **Set Up the Ratios**:
- From the first part of the question, the ratio of the speed of the stream to the speed of the first boat is given as \( \frac{y}{x} = \frac{2}{5} \).
- From this, we can express \( y \) in terms of \( x \):
\[ y = \frac{2}{5}x \]

3. **Set Up the Second Ratio**:
- The ratio of the speed of the stream to the speed of the second boat is given as \( \frac{y}{p} = \frac{3}{4} \).
- From this, we can express \( y \) in terms of \( p \):
\[ y = \frac{3}{4}p \]

4. **Equate the Two Expressions for \( y \)**:
- Since both expressions equal \( y \), we can set them equal to each other:
\[ \frac{2}{5}x = \frac{3}{4}p \]

5. **Cross Multiply to Solve for the Ratio**:
- Cross multiplying gives us:
\[ 2 \cdot 4x = 3 \cdot 5p \]
\[ 8x = 15p \]

6. **Find the Ratio of \( x \) to \( p \)**:
- Rearranging the equation gives:
\[ \frac{x}{p} = \frac{15}{8} \]

7. **Conclusion**:
- Therefore, the ratio of the speeds of the first boat to the second boat in still water is:
\[ \text{Ratio of first boat to second boat} = 15 : 8 \]

### Final Answer:
The ratio of the speeds of the first boat to the second boat in still water is \( 15 : 8 \).

---