Two trains started at the same time, one from A to B and the other from B to A. If they arrived at B and A respectively 25 hours and 36 hours after they passed each other, the ratio of the speeds of the two trains was:

Options

A. `2:4`
B. `3:2`
C. `6:5`
D. `3:4`

Answer

To solve the problem, we need to find the ratio of the speeds of the two trains based on the time they take to reach their respective destinations after passing each other.

### Step-by-Step Solution:

1. **Understanding the Problem**:
- Let the speed of the train from A to B be \( S_1 \).
- Let the speed of the train from B to A be \( S_2 \).
- After the trains meet, the train from A to B takes 25 hours to reach B.
- The train from B to A takes 36 hours to reach A.

2. **Using the Concept of Speed and Time**:
- The distance covered by each train after they meet can be expressed in terms of speed and time:
- Distance covered by Train 1 (from A to B) = \( S_1 \times 25 \)
- Distance covered by Train 2 (from B to A) = \( S_2 \times 36 \)

3. **Setting Up the Relationship**:
- Since both trains cover the same distance after they meet (the distance between the meeting point and their respective destinations), we can equate the two distances:
\[ S_1 \times 25 = S_2 \times 36 \]

4. **Rearranging the Equation**:
- Rearranging the equation gives us:
\[ \frac{S_1}{S_2} = \frac{36}{25} \]

5. **Finding the Ratio**:
- To express this ratio in simplest form, we can write:
\[ \frac{S_1}{S_2} = \frac{36}{25} \implies S_1 : S_2 = 36 : 25 \]

6. **Final Ratio**:
- The ratio of the speeds of the two trains is \( 36 : 25 \).

### Conclusion:
The ratio of the speeds of the two trains is \( 36 : 25 \).