A 255-m long train is running at a speed of 72 km/h. It crosses a platform of length 745 m in:

The correct option is 50 seconds.

To find the time taken by the train to cross the platform, we first need to determine the total distance that the train has to cover.

Step 1: Calculate the total distance to cover
When a train crosses a platform, it must cover a distance equal to the sum of its own length and the length of the platform.

$\text{Total Distance}=\text{Length of Train}+\text{Length of Platform}$

$\text{Total Distance}=255\text{m}+745\text{m}=1000\text{m}$

Step 2: Convert the speed of the train from km/h to m/s
The given speed of the train is 72 km/h. Since the distance is in meters and the required time is in seconds, we convert the speed into meters per second (m/s) by multiplying by $\frac{5}{18}$.

$\text{Speed}=72\×\frac{5}{18}\text{m/s}$

$\text{Speed}=4\×5\text{m/s}=20\text{m/s}$

Step 3: Calculate the time taken
Using the formula connecting distance, speed, and time:

$\text{Time}=\frac{\text{Total Distance}}{\text{Speed}}$

$\text{Time}=\frac{1000}{20}\text{seconds}=50\text{seconds}$

Therefore, the train crosses the platform in 50 seconds.