$A$ 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 $km/h$):

$A$ person has to travel from point $A$ to point $B$ in a certain time. Travelling at a speed of $5 \, km/h$,he reaches $48 \, min$ late,and while travelling at a speed of $8 \, km/h$,he reaches $15 \, min$ early. What is the distance from point $A$ to $B$ (in $km$)?

The bus fare for one person is $Rs. 420$ from Agra to Aligarh and the train fare between the same places for one person is equal to $\frac{3}{4}$ of the bus fare for $2$ persons between the same places. What is the total fare paid by $2$ persons traveling by bus and $4$ persons traveling by train between the two places? (in $Rs.$)

$A$ thief steals a car at $2.30$ $p.m.$ and drives it at $60\, km/h$. The theft is discovered at $3.00$ $p.m.$ and the owner sets off in another car at $75\, km/h$. When will he overtake the thief? (in $p.m.$)

Excluding stoppages, the speed of a bus is $54 \, km/h$ and including stoppages, it is $45 \, km/h$. For how many minutes does the bus stop per hour?

$A$ train $50\, m$ long passes a platform $100\, m$ long in $10\, s$. The speed of the train in $m/s$ is: