Train A crosses a pole in 25 sec. and train B crosses a pole in 1 min 15 sec. Length of train A is half of the length of train B. Find out the ratio of speed of A & B ?

Options

A. `3 : 2`
B. `2 : 3`
C. `3 : 1`
D. `5 : 3`

Answer

To solve the problem, we need to find the ratio of the speeds of Train A and Train B based on the information given about their lengths and the time taken to cross a pole.

### Step-by-Step Solution:

1. **Define the Lengths of the Trains:**
- Let the length of Train A be \( x \).
- Since the length of Train A is half of Train B, the length of Train B will be \( 2x \).

2. **Convert Time to Seconds:**
- Train A crosses a pole in 25 seconds.
- Train B crosses a pole in 1 minute 15 seconds, which is \( 60 + 15 = 75 \) seconds.

3. **Calculate the Speed of Train A:**
- Speed is defined as distance divided by time.
- For Train A, the speed \( S_A \) can be calculated as:
\[ S_A = \frac{\text{Length of Train A}}{\text{Time taken by Train A}} = \frac{x}{25} \]

4. **Calculate the Speed of Train B:**
- For Train B, the speed \( S_B \) can be calculated as:
\[ S_B = \frac{\text{Length of Train B}}{\text{Time taken by Train B}} = \frac{2x}{75} \]

5. **Find the Ratio of Speeds:**
- Now, we need to find the ratio of the speeds of Train A and Train B:
\[ \text{Ratio} = \frac{S_A}{S_B} = \frac{\frac{x}{25}}{\frac{2x}{75}} \]
- Simplifying the ratio:
\[ \text{Ratio} = \frac{x}{25} \times \frac{75}{2x} = \frac{75}{50} = \frac{3}{2} \]

6. **Final Result:**
- The ratio of the speed of Train A to the speed of Train B is \( 3:2 \).