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/hr. What is the length of the platform ? (in m).

Hint: For solving these types of problems; Speed distance-time relation formulae and understanding the given question and drawing a rough sketch based on the given question are required.

Complete step by step solution:
Let's solve the given question!!!
Given, speed of train \[\text{=54}\]km/h
But; we need answers in meters given.
So; we have to convert km/hr to m/s.
We know that; \[\text{1 km/hr =}\dfrac{\text{5}}{\text{18}}\text{m/s}\]
\[\Rightarrow \]Speed of train\[=\dfrac{5}{18}\times 54m/s=15m/s\]
Rough sketch:

Let ‘x’ be the length of the platform.
Let ‘y' be the length of the train.
We know that; \[\text{speed=}\dfrac{\text{distance}}{\text{time}}\]
Given that the train crosses the man standing on the platform in\['20'\sec \]
\[\Rightarrow \]Length of train\['y'=(speed)\times (time)\]
\[=(15m/s)\times (20s)\]
\[\therefore \]Length of train \[;y=300\]
Now; Given that the train passes the station platform in \[36\]seconds.
So, the distance becomes \[\to x+y\]
Because, if a train crosses the platform it have to pass over the platform completely along with it
Now; use \[\text{speed=}\dfrac{\text{distance}}{\text{time}}\]
\[\Rightarrow 15m/s=\dfrac{x+y}{36\sec }\]
\[\Rightarrow 15m/s=\dfrac{x+300m}{36\operatorname{s}}\]
\[\Rightarrow (15m/s)\times (36s)=x+300m\]
\[\Rightarrow 540m=x+300m\]
\[\Rightarrow x=(540m)-(300m)\]
\[x=240m\]
Therefore; Length of the platform \['x'=240m\]

Note: Remember! a good understanding of questions and a rough diagram are most important!!!
As we mentioned that \[\text{1 km/hr =}\dfrac{\text{5}}{\text{18}}\text{m/s}\]
We can explain it by using general conversion of km to m and hr to sec.
$1km=1000m\,,\,1hr\,=\,3600\,\sec $
Hence we can write
$\Rightarrow 1km/hr=\dfrac{1000}{3600}m/\sec $
We can simplify it by dividing numerator and denominator by 200.