$A$ train leaves station $A$ at $7 \, am$ and reaches station $B$ at $11 \, am$. Another train leaves station $B$ at $8 \, am$ and reaches station $A$ at $11.30 \, am$. At what time do the two trains cross each other?

It takes $8\, hours$ for a $600\, km$ journey,if $120\, km$ is done by train and the rest by car. It takes $20\, minutes$ more,if $200\, km$ is done by train and the rest by car. The ratio of the speed of the train to that of the car is

$A$ train covers a distance between station $A$ and station $B$ in $45 \, min$. If the speed of the train is reduced by $5 \, km/h$,then the same distance is covered in $48 \, min$. The distance between stations $A$ and $B$ is? (in $km$)

In a race of $800\, m,$ $A$ can beat $B$ by $40\, m$. In a race of $500\, m,$ $B$ can beat $C$ by $5\, m$. In a race of $200\, m,$ $A$ will beat $C$ by? (in $m$)

$A, B$ and $C$ start at the same time in the same direction to run around a circular stadium. $A$ completes a round in $252 \text{ seconds}$,$B$ in $308 \text{ seconds}$ and $C$ in $198 \text{ seconds}$,all starting at the same point. After what time will they next meet at the starting point again?

$A$ goods train and a passenger train are running on parallel tracks in the same direction. The driver of the goods train observes that the passenger train coming from behind overtakes and crosses his train completely in $60 \, s$. Whereas a passenger on the passenger train marks that he crossed the goods train in $40 \, s$. If the speeds of the trains are in the ratio of $1:2$,find the ratio of their lengths.