An express train completely crosses a platform that is 300 m long in 30 seconds. Find the speed of the train if it passes a person jogging in the opposite direction at a speed of 12 m/sec.

The correct option is Cannot be determined.

Step-by-step explanation:

Let the length of the train be $L$ meters and the speed of the train be $v$ m/sec.

When a train completely crosses a platform, the total distance covered by the train is equal to the sum of the length of the train and the length of the platform.

Given that the length of the platform is $300$ meters and the train takes $30$ seconds to cross it, we can write the equation using the formula $\text{Distance}=\text{Speed}\times \text{Time}$:

$L+300=30v$

Rearranging this equation gives:

$L=30v-300$

Notice that we have one equation with two unknown variables, $L$ and $v$.

To find the value of $v$ (the speed of the train), we require a second independent equation. Although the question mentions that the train passes a person jogging in the opposite direction at a speed of $12$ m/sec, the time taken by the train to pass this person is not provided.

Without knowing the time taken to pass the person (or the length of the train $L$), it is impossible to set up a second equation to solve for $v$.

Therefore, the speed of the train cannot be determined from the given data.