Two trains of equal length take $10\, seconds$ and $15\, seconds$ respectively to cross a telegraph post. If the length of each train is $120\, metres,$ in what time (in $seconds$) will they cross each other when travelling in opposite directions?

Paschim Express left Delhi for Mumbai at $14:30\, \text{hours}$ travelling at a speed of $60\, \text{km/h}$. August Kranti Express left Delhi for Mumbai on the same day at $16:30\, \text{hours}$ travelling at a speed of $80\, \text{km/h}$. How far away from Delhi will the two trains meet (stoppages excluded)? (in $\text{km}$)

$A$ bus started its journey from Bettiah and reached Motihari in $44 \, \text{min}$ with an average speed of $50 \, \text{km/h}$. If the average speed of the bus is increased by $5 \, \text{km/h}$, how much time will it take to cover the same distance? (in $\text{min}$)

$A$ truck covers a distance of $396 \, km$ in $5 \, hours \, 30 \, minutes$. The average speed of a bike is $\frac{4}{3}$ of the average speed of the truck. What is the time taken by the bike to cover a distance of $12 \, km$ less than the distance covered by the truck?

$A$ car travels $80 \, km$ in $2 \, hours$ and a train travels $80 \, km$ in $3 \, hours$. The ratio of the speed of the car to that of the train is

$A$ boy rides his bicycle $10 \, km$ at an average speed of $12 \, km/hr$ and again travels $12 \, km$ at an average speed of $10 \, km/hr$. His average speed for the entire trip is approximately (in $km/hr$)