Aditya is travelling on his cycle and has calculated that he will reach point $A$ at $2\, pm$, if he travels at $10\, km/h$. He will reach there at $12\, noon$, if he travels at $15\, km/h$. At what speed must he travel to reach $A$ at $1\, pm$? (in $km/h$)

Without any stoppage, a person travels a certain distance at an average speed of $42 \, km/h$ and with stoppages he covers the same distance at an average speed of $28 \, km/h$. How many minutes per hour does he stop?

$A$ train leaves the station $1 \, hr$ before the scheduled time. The driver decreases its speed by $4 \, km/hr$. At the next station $120 \, km$ away,the train reaches on time. Find the original speed of the train in $km/hr$.

$A$ motorcyclist left $6 \frac{2}{3}$ minutes later than the scheduled time,but in order to reach his destination $21 \, km$ away on time,he had to increase his speed by $12 \, km/h$ from his usual speed. What is the usual speed (in $km/h$) of the motorcyclist?

Two trains start at the same time from two stations and proceed towards each other at the speeds of $20 \, km/h$ and $25 \, km/h$ respectively. When they meet,it is found that one train has travelled $80 \, km$ more than the other. Find the distance between the two stations (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 $m$)