A train travelling at 48 km/h completely crosses another train having half the length of first train and travelling in opposite direction at 42 km/h in 12 seconds. The train having speed 48 km/h also passes a railway platform in 45 seconds. What is the length of the platform ?

Assume the length of the first train to be $$x$$ m

So, the length of the second train is $$0.5x$$ m

The total length to be covered = $$1.5x$$ m

As they are travelling in the opposite directions, their speed will add in relative frame

So, the combined speed is $$48+42\ =\ 90\ $$kmph or $$\ 90\times\dfrac{5}{18}=25$$ m/s

So, $$\dfrac{1.5x}{25}=12$$

$$1.5x=300$$

or, $$x=200$$ m

Given it passes the station in 45 sec

Let the length of the station be $$l$$ m

So, $$\dfrac{l+x}{48\times\dfrac{5}{18}}=45$$

$$l+x=600$$

$$l=400$$ m

Hence, the answer is 400 m