A train passes over a 400m long bridge. If the speed of the traIN IS 30M/S and the train takes 20 s to cross the brigde , then the length of the train is

Options

A. 400 m
B. 600 m
C. 800 m
D. 200 m

Explanation

To find the length of the train that crosses a 400m long bridge in 20 seconds at a speed of 30m/s, we can follow these steps:

### Step-by-Step Solution:

1. **Calculate the total distance traveled by the train while crossing the bridge**:
- The formula to calculate distance is:
\[ \text{Distance} = \text{Speed} \times \text{Time} \]
- Here, the speed of the train is 30 m/s and the time taken to cross the bridge is 20 seconds.
- Therefore, the total distance traveled by the train is:
\[ \text{Distance} = 30 \, \text{m/s} \times 20 \, \text{s} = 600 \, \text{m} \]

2. **Understand the relationship between the distance traveled, the length of the train, and the length of the bridge**:
- When the train crosses the bridge, it covers its own length plus the length of the bridge.
- Let \( L \) be the length of the train. The total distance traveled can be expressed as:
\[ \text{Total Distance} = \text{Length of Train} + \text{Length of Bridge} \]
- Given that the length of the bridge is 400 m, we can write:
\[ 600 \, \text{m} = L + 400 \, \text{m} \]

3. **Solve for the length of the train**:
- Rearranging the equation gives:
\[ L = 600 \, \text{m} - 400 \, \text{m} \]
- Therefore:
\[ L = 200 \, \text{m} \]

### Final Answer:
The length of the train is **200 meters**.