Two trains are running in opposite directions with the same speed. If the length of each train is $135 \, m$ and they cross each other in $18 \, s$,the speed of each train is (in $km/h$):

$A$ train running at a speed of $40 \, m/s$ crosses a pole in $21 \, s$ less than the time it requires to cross a bridge $3.5$ times its length at the same speed. What is the length of the bridge (in $m$)?

Starting from his house,a student walks at a speed of $2.5 \, km/hr$ and reaches his school $6 \, minutes$ late. Next day he increases his speed by $1 \, km/hr$ and reaches the school $6 \, minutes$ early. How far is the school from his house? (in $km$)

$A$ starts from a place $P$ to go to a place $Q$. At the same time $B$ starts from $Q$ to $P$. If after meeting each other $A$ and $B$ took $16$ and $25$ $hours$ more respectively to reach their destinations,the ratio of their speeds 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 $km$.

If a person walks at $14 \, km/hr$ instead of $10 \, km/hr$,he would have walked $20 \, km$ more. The actual distance travelled by him is (in $km$)