Two trains start at the same time from points x and y towards each other and after crossing , they take 9 h and 4 h in reaching points y and x ,respectively. Find the ratio of speeds of the 1st train to that of the 2nd train.

Options

A. a. `2:3`
B. b. `3:2`
C. c. `2:5`
D. d. `5:3`

Answer

To solve the problem of finding the ratio of the speeds of the two trains, we can use the relationship between speed, distance, and time.

### Step-by-Step Solution:

1. **Understanding the Problem**:
- Train A starts from point X and travels towards point Y.
- Train B starts from point Y and travels towards point X.
- After crossing each other, Train A takes 9 hours to reach point Y, and Train B takes 4 hours to reach point X.

2. **Let the Speeds be Represented**:
- Let the speed of Train A (from X to Y) be \( S_A \).
- Let the speed of Train B (from Y to X) be \( S_B \).

3. **Using the Concept of Distance**:
- The distance covered by Train A after crossing is \( D_A = S_A \times 9 \) (since it takes 9 hours to reach Y).
- The distance covered by Train B after crossing is \( D_B = S_B \times 4 \) (since it takes 4 hours to reach X).

4. **Setting the Distances Equal**:
- At the point of crossing, both trains have covered the same distance from their starting points to the crossing point. Therefore, we can set the distances equal:
\[ D_A = D_B \]
\[ S_A \times 9 = S_B \times 4 \]

5. **Rearranging the Equation**:
- Rearranging gives us:
\[ \frac{S_A}{S_B} = \frac{4}{9} \]

6. **Finding the Ratio**:
- The ratio of the speeds of Train A to Train B is:
\[ S_A : S_B = 4 : 9 \]

### Final Answer:
The ratio of the speeds of the first train to that of the second train is \( 4 : 9 \).