If a 200 m long train crosses a platform of the same length as that of the train in 20 seconds, the speed of the train is:

Options

A. 50 km/hr
B. 60 km/hr
C. 72 km/hr
D. 80 km/hr

Answer

To solve the problem, we need to find the speed of the train when it crosses a platform of the same length (200 meters) in 20 seconds.

### Step-by-Step Solution:

1. **Identify the Lengths**:
The length of the train is 200 meters, and the length of the platform is also 200 meters.

2. **Calculate the Total Distance**:
When the train crosses the platform, it needs to cover its own length plus the length of the platform.
\[ \text{Total Distance} = \text{Length of Train} + \text{Length of Platform} = 200 \, \text{m} + 200 \, \text{m} = 400 \, \text{m} \]

3. **Determine the Time Taken**:
The time taken to cross the platform is given as 20 seconds.

4. **Calculate the Speed**:
Speed is defined as the distance traveled divided by the time taken.
\[ \text{Speed} = \frac{\text{Total Distance}}{\text{Time}} = \frac{400 \, \text{m}}{20 \, \text{s}} = 20 \, \text{m/s} \]

5. **Convert Speed to Kilometers per Hour**:
To convert the speed from meters per second to kilometers per hour, we use the conversion factor \( 1 \, \text{m/s} = 3.6 \, \text{km/h} \).
\[ \text{Speed in km/h} = 20 \, \text{m/s} \times 3.6 = 72 \, \text{km/h} \]

### Final Answer:
The speed of the train is **72 kilometers per hour**.