In a $1 \, km$ race,$A, B$,and $C$ are three participants. $A$ can give $B$ a start of $50 \, m$ and $C$ a start of $69 \, m$. The start,which $B$ can allow $C$ is (in $m$):

$A$ car covers four successive $7 \, km$ distances at speeds of $10 \, km/h$,$20 \, km/h$,$30 \, km/h$,and $60 \, km/h$ respectively. Its average speed over this total distance is (in $km/h$):

The fare of a bus is $Rs. X$ for the first five kilometres and $Rs. 13$ per kilometer thereafter. If a passenger pays $Rs. 2402$ for a journey of $187$ kilometres,what is the value of $X$? (in $Rs.$)

$A$ 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 $km$):

$A$ man leaves a point $P$ and reaches the point $Q$ in $4 \, hours$. Another man leaves the point $Q$,$2 \, hours$ earlier and reaches the point $P$ in $4 \, hours$. Find the time in which the first man meets the second man (in $hours$).

$A$ gun is fired at a distance of $1.34$ $km$ from Geeta. She hears the sound after $4$ $sec$. The speed at which sound travels is (in $m/sec$):