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 $cm$):

Train $A$ starts its journey from Patna to Hazipur while train $B$ starts from Hazipur to Patna. After crossing each other, they finish their journey in $81\, \text{hours}$ and $121\, \text{hours}$ respectively. What will be the speed of train $B$ if the speed of train $A$ is $44\, \text{km/h}$?

$A$ truck covers a distance of $550 \, m$ in $1 \, min$,whereas a bus covers a distance of $33 \, km$ in $45 \, min$. The ratio of their speeds is

$A$ 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?

Sound travels $330 \text{ m/s}$. If the sound of a thundercloud is heard $10 \text{ s}$ after the flash,the distance of the thundercloud is (in $\text{km}$):

$A$ and $B$ are two stations. $A$ train goes from $A$ to $B$ at $64 \text{ km/h}$ and returns to $A$ at a slower speed. If its average speed for the whole journey is $56 \text{ km/h}$,at what speed did it return? (in $\text{km/h}$)