$A$ train travelling at a speed of $55\, km/hr$ travels from place $X$ to place $Y$ in $4\, hours$. If its speed is increased by $5\, km/hr$,then the time of journey is reduced by (in $minutes$):

$A$ man covers a certain distance between his house and office on a scooter. With an average speed of $30 \, km/hr$,he is late by $10 \, min$. However,with a speed of $40 \, km/hr$,he reaches his office $5 \, min$ earlier. Find the distance between his house and office in $km$.

$A$ boy started from his house by bicycle at $10:00 \, am$ at a speed of $12 \, km/h$. His elder brother started after $1 \, hour \, 15 \, minutes$ by scooter along the same path and caught him at $1:30 \, pm$. The speed of the scooter was (in $km/h$):

$A$ car completes a journey in $6\, hours$. It covers half the distance at $50\, km/h$ and the rest at $70\, km/h$. The length of the journey is (in $km$):

The distance between places $A$ and $B$ is $999 \text{ km}$. An express train leaves place $A$ at $6:00 \text{ am}$ and runs at a speed of $55.5 \text{ km/h}$. The train stops on the way for $1 \text{ hour } 20 \text{ minutes}$. At what time does it reach place $B$ (in $\text{pm}$)?

$A$ car travels from $P$ to $Q$ at a constant speed. If its speed were increased by $10 \, km/h$,it would have taken $1 \, hour$ less to cover the distance. It would have taken a further $45 \, minutes$ less if the speed was increased by another $10 \, km/h$. The distance between the two cities is (in $km$):