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 $m$):

Three men step off together from the same spot. Their steps measure $63 \, cm$,$70 \, cm$,and $77 \, cm$ respectively. The minimum distance each should cover so that all can cover the distance in complete steps is (in $cm$):

Two trains of lengths $120 \,m$ and $80 \,m$ are running in the same direction with velocities of $40 \,km/h$ and $50 \,km/h$ respectively. The time taken by them to cross each other is (in $sec$).

Mohan covers $10.2 \, km$ in $3 \, hours$. The distance covered by him in $5 \, hours$ is (in $km$):

$A$ boy walking at a speed of $10\, km/hr$ reaches his school $15\, minutes$ late. Next time he increases his speed by $2\, km/hr$, but still he is late by $5\, minutes$. Find the distance of his school from his house (in $km$).

$A$ $100\, m$ long train completely passes a man walking in the same direction at $6\, km/h$ in $5\, s$ and also a car travelling in the same direction in $6\, s$. At what speed was the car travelling? (in $km/h$)