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 $m$)

$A$ man starts from a place $P$ and reaches the place $Q$ in $7 \, hours$. He travels $\frac{1}{4}^{th}$ of the distance at $10 \, km/h$ and the remaining distance at $12 \, km/h$. The distance,in $km$,between $P$ and $Q$ is

$A$ car travelling with $\frac{5}{7}$ of its actual speed covers $42 \, km$ in $1 \, hour \, 40 \, minutes \, 48 \, seconds.$ Find the actual speed of the car (in $km/hr$).

$A$ man covered a certain distance at some speed. Had he moved $3 \text{ km/hr}$ faster,he would have taken $40 \text{ minutes}$ less. If he had moved $2 \text{ km/hr}$ slower,he would have taken $40 \text{ minutes}$ more. The distance (in $\text{km}$) is:

$A$ man starts running from point $P$ at $11:00$ $a.m.$ with a speed of $10 \, km/hr$. He runs for $2 \, hours$ and then takes a $1 \, hour$ rest. He continues this pattern until he is caught by another man who starts at $2:00 \, p.m.$ from point $P$ and runs non-stop at a speed of $15 \, km/hr$ toward the first man. At what time (in $p.m.$) will the first man be caught?

In covering a certain distance,the speeds of $A$ and $B$ are in the ratio of $3:4$. $A$ takes $30 \text{ minutes}$ more than $B$ to reach the destination. What is the time taken by $A$ to reach the destination (in hours)?