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 friends started for a place,one by motorcycle and the other by train. The speed of the motorcycle is $30 \, km/h$ and that of the train is $24 \, km/h$. The first one takes $6 \, hr \, 12 \, min$ to reach the destination. Find the time taken by the second one to reach the destination (in $hr$).

Two men $A$ and $B$ start from a place $P$ walking at $3 \, km/h$ and $3.5 \, km/h$ respectively. How many $km$ will they be apart at the end of $3 \, h$,if they walk in opposite directions (in $.5$)?

$A$ horse rider travels on horseback from Bhopal to Chandigarh at a constant speed. If the horse increased its speed by $6 \, km/h$,it would take the rider $4 \, hours$ less to cover that distance. If the horse travelled at a speed $6 \, km/h$ lower than the initial speed,it would take him $10 \, hours$ more than the time he would have taken if he had travelled at a speed $6 \, km/h$ higher than the initial speed. Find the distance between Bhopal and Chandigarh in $km$.

$A$ car driver leaves Bangalore at $8:30 \, am$ and expects to reach a place $300 \, km$ from Bangalore at $12:30 \, pm$. At $10:30 \, am$, he finds that he has covered only $40 \%$ of the distance. By how much does he have to increase the speed of the car in order to keep up with his schedule? (in $km/h$)

The distance between two cities $A$ and $B$ is $330\, km$. $A$ train starts from $A$ at $8\, a.m.$ and travels towards $B$ at $60\, km/hr$. Another train starts from $B$ at $9\, a.m.$ and travels towards $A$ at $75\, km/hr$. At what time do they meet? (in $a.m.$)