Length of a train and that of a platform are equal. If with a speed of $135 \; km/hr$,the train crosses the platform in $40 \; seconds$,then the length (in $m$) of the train is:

$A$ train $125 \;m$ long passes a man,running at $5 \;km/hr$ in the same direction in which the train is going,in $10 \;seconds$. The speed of the train is (in $km/hr$):

$A$ train $120 \; m$ long moving at a speed of $60 \; km/hr$ crosses a train $130 \; m$ long coming from the opposite direction in $6 \; seconds$. The speed of the second train is (in $km/hr$):

Two trains running at the rate of $45 \; km/h$ and $36 \; km/h$ respectively,on parallel tracks in opposite directions,are observed to pass each other in $8 \; seconds$. When they are running in the same direction at the same rate as before,a person sitting in the faster train observes that he passes the other in $30 \; seconds$. Find the length of the trains (in $m$).

Two trains $140 \; m$ and $160 \; m$ long run at a speed of $60 \; km/hr$ and $40 \; km/hr$ respectively in opposite directions on parallel tracks. The time (in $seconds$) which they take to cross each other is:

$A$ train passes a station platform in $36 \; \text{seconds}$ and a man standing on the platform in $20 \; \text{seconds}$. If the speed of the train is $54 \; \text{km/hr}$, what is the length (in $m$) of the platform?