The diameter of each wheel of a car is $70 \, cm$. If each wheel rotates $400 \, \text{times per minute}$, then the speed of the car (in $km/hr$) is $\left( \text{Take } \pi = \frac{22}{7} \right)$.

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 $cm$):

$A$ train passes through a telegraph post in $9$ $seconds$ moving at a speed of $54 \, km/h$. The length of the train is (in $meters$):

Two trains start from $P$ and $Q$ respectively and travel towards each other at a speed of $50\, km/hr$ and $40\, km/hr$ respectively. By the time they meet,the first train has travelled $100\, km$ more than the second. The distance between $P$ and $Q$ is (in $km$):

$A$ policeman starts to chase a thief. When the thief goes $10 \, \text{steps}$, the policeman moves $8 \, \text{steps}$. $5 \, \text{steps}$ of the policeman are equal to $7 \, \text{steps}$ of the thief. The ratio of the speeds of the policeman and the thief is

$A$ 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 $km$.