A express freight train measuring 240 m in length passes a station platform in 45 seconds and passes a light pole in 15 seconds. What is the length of the platform?

Correct Option: 480 m

Step-by-Step Explanation:

To find the length of the station platform, we can break the problem down into two simple steps: first, determining the speed of the train as it passes the light pole, and second, calculating the length of the platform using the total distance covered while passing it.

Step 1: Find the speed of the train

When a train passes a point object with negligible length (such as a light pole), the total distance covered by the train is equal to the length of the train itself.

Given:

Length of the train, $L_{\text{train}}=240\text{m}$

Time taken to pass the pole, $t_{\text{pole}}=15\text{s}$

Using the speed formula:

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

$\text{Speed}=\frac{240}{15}=16\text{m/s}$

Thus, the speed of the train is 16 m/s.

Step 2: Calculate the length of the platform

When a train passes an object of significant length (like a station platform), the total distance covered is the sum of the length of the train and the length of the platform.

Let $L_{\text{platform}}$ be the length of the platform.

Total time taken to pass the platform, $t_{\text{platform}}=45\text{s}$

Using the distance formula:

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

$\text{Total Distance}=16\times 45=720\text{m}$

We know that:

$\text{Total Distance}=L_{\text{train}}+L_{\text{platform}}$

Substituting the values into the equation:

$720=240+L_{\text{platform}}$

$L_{\text{platform}}=720-240=480\text{m}$

Conclusion:
The length of the platform is 480 m.