A train crosses a bridge of length 150 m in 15 s and a man standing on it in 9 s. The train is travelling at a uniform speed. Length of the train is

Options

A. 225m
B. 200m
C. 135 m
D. 90 m

Answer

To solve the problem step by step, we will break down the information given and use it to find the length of the train.

### Step-by-Step Solution:

1. **Identify the Given Information:**
- Length of the bridge = 150 m
- Time taken to cross the bridge = 15 s
- Time taken to cross a man standing on the train = 9 s

2. **Define Variables:**
- Let the length of the train be \( L \) meters.
- Let the speed of the train be \( y \) meters per second.

3. **Calculate the Speed of the Train:**
- When the train crosses the bridge, it covers a distance equal to the length of the bridge plus the length of the train. Therefore, the distance covered while crossing the bridge is:
\[ \text{Distance} = \text{Length of the bridge} + \text{Length of the train} = 150 + L \]
- The time taken to cross this distance is 15 seconds. Using the formula:
\[ \text{Speed} = \frac{\text{Distance}}{\text{Time}} \]
we can write:
\[ y = \frac{150 + L}{15} \]

4. **Calculate the Length of the Train Using the Time to Cross a Man:**
- When the train crosses a man, it only covers its own length \( L \) in 9 seconds. Thus, we have:
\[ y = \frac{L}{9} \]

5. **Set Up the Equations:**
- From the first equation:
\[ 15y = 150 + L \quad \text{(1)} \]
- From the second equation:
\[ L = 9y \quad \text{(2)} \]

6. **Substitute Equation (2) into Equation (1):**
- Substitute \( L \) from equation (2) into equation (1):
\[ 15y = 150 + 9y \]
- Rearranging gives:
\[ 15y - 9y = 150 \]
\[ 6y = 150 \]
\[ y = 25 \text{ m/s} \]

7. **Find the Length of the Train:**
- Now substitute \( y \) back into equation (2) to find \( L \):
\[ L = 9y = 9 \times 25 = 225 \text{ m} \]

### Final Answer:
The length of the train is **225 meters**.