120 meter long train is running at a speed of 90 km per hour. It will cross a railway platform 230 m long in :

Options

A. `4(4)/(5)` seconds
B. `9(1)/(5)` seconds
C. 7 seconds
D. 14 seconds

Answer

To solve the problem of how long it takes for a 120-meter long train traveling at a speed of 90 km/h to cross a 230-meter long railway platform, we can follow these steps:

### Step-by-Step Solution:

1. **Understand the Problem**:
- We have a train that is 120 meters long.
- The train is moving at a speed of 90 km/h.
- The platform is 230 meters long.
- We need to find out how long it takes for the train to completely cross the platform.

2. **Calculate the Total Distance to be Covered**:
- The total distance that the train needs to cover to completely cross the platform is the length of the train plus the length of the platform.
- Total Distance = Length of Train + Length of Platform
- Total Distance = 120 m + 230 m = 350 m

3. **Convert Speed from km/h to m/s**:
- The speed of the train is given in kilometers per hour (km/h). We need to convert this to meters per second (m/s) for consistency in units.
- The conversion factor is:
\[ 1 \text{ km/h} = \frac{5}{18} \text{ m/s} \]
- Therefore,
\[ \text{Speed} = 90 \text{ km/h} \times \frac{5}{18} = 25 \text{ m/s} \]

4. **Calculate the Time Taken to Cross the Platform**:
- We can use the formula for time, which is:
\[ \text{Time} = \frac{\text{Distance}}{\text{Speed}} \]
- Substituting the values we have:
\[ \text{Time} = \frac{350 \text{ m}}{25 \text{ m/s}} = 14 \text{ seconds} \]

5. **Final Answer**:
- The time taken for the train to cross the railway platform is 14 seconds.