A train passes a station platform in 36 seconds and a man standing on the platform in 20 seconds. If the speed of the train is 54 km/h, then find the length of the platform.

We have two parameters to look at in this question:

1) Length of the train. Let this be assumed to be a metres.

2) Length of the platform. Let us assume it as b metres.

It is given that speed of the train is 54 km/h Or, 54$$\ \times\ \frac{\ 5}{18}$$= 15 m/s

So, when it passes the man, distance covered will be the length of the train itself= a metres.

So, time taken= $$\frac{Dis\tan ce}{Speed}=\ \ \frac{\ a}{15}$$, which is given to be 20 seconds.

So, $$\frac{\ a}{15}=20$$. And a= 300 metres.

Now, to pass the entire platform, we need to account for both the length of the platform and that of the train.

So, effective distance to be covered= a+b= 300+b metres.

Speed of the train = 15 m/s.

So, time taken= $$\frac{\ 300+b}{15}$$, which is given to be 36 seconds.

So, $$\frac{\ 300+b}{15}=36$$

=>$$\ 300+b=36\times\ 15$$

=>b=540-300

So, b= Length of the train= 240 metres.