$A$ train running at the speed of $66 \, km/h$ crosses a signal pole in $18 \, seconds$. What is the length of the train (in $m$)?

$A, B$ and $C$ start together from the same place to walk around a circular path of length $12 \, km$. $A$ walks at the rate of $4 \, km/h$,$B$ at $3 \, km/h$,and $C$ at $\frac{3}{2} \, km/h$. They will meet together at the starting place at the end of (in $h$):

$A$ man travelled from the village to the post office at the rate of $25 \, km/hr$ and walked back at the rate of $4 \, km/hr$. If the whole journey took $5 \, hours \, 48 \, minutes$,find the distance of the post office from the village (in $km$).

$A$ man walks at the rate of $5 \, km/hr$ for $6 \, hours$ and at $4 \, km/hr$ for $12 \, hours$. The average speed of the man (in $km/hr$) is:

$A$ man travelled a distance of $61 \, km$ in $9 \, h$,partly on foot at the rate of $4 \, km/h$ and partly on bicycle at the rate of $9 \, km/h$. The distance travelled on foot was (in $km$):

$A$ man standing on a railway platform observes that a train going in one direction takes $4 \,seconds$ to pass him. Another train of the same length going in the opposite direction takes $5 \,seconds$ to pass him. The time taken (in $seconds$) by the two trains to cross each other will be: