A train moving at a speed of 63 km/hr enters a railway station and crosses the platform in 20 s. If the length of the train is 100 m, what is the length of the platform?

The correct option is 250 m.

To find the length of the platform, we can follow these step-by-step calculations:

Step 1: Convert the speed of the train from km/hr to m/s
The speed of the train is given as 63 km/hr. To convert this speed into meters per second (m/s), we multiply by the conversion factor $\frac{5}{18}$:

$\text{Speed}=63\times \frac{5}{18}\text{ m/s}$

Simplifying the expression (dividing 63 and 18 by their greatest common divisor, 9):

$\text{Speed}=7\times \frac{5}{2}=\frac{35}{2}=17.5\text{ m/s}$

Step 2: Understand the total distance covered
When a train crosses a platform, the total distance it covers is the sum of the length of the train and the length of the platform.
Let $L$ be the length of the platform in meters.
The length of the train is given as 100 m. Therefore:

$\text{Total Distance}=\text{Length of Train}+\text{Length of Platform}=100+L$

Step 3: Relate distance, speed, and time
Using the formula:

$\text{Distance}=\text{Speed}\times \text{Time}$

We are given that the train crosses the platform in 20 seconds. Substituting the known values into the formula:

$100+L=17.5\times 20$

Step 4: Solve for the length of the platform ($L$)
Calculate the product on the right side of the equation:

$100+L=350$

Subtract 100 from both sides:

$L=350-100$

$L=250\text{ m}$

Thus, the length of the platform is 250 m.