$A$ boy is running at a speed of $p \, km/h$ to cover a distance of $1 \, km$. However,due to the slippery ground,his speed is reduced by $q \, km/h$ $(p > q)$. If he takes $r$ hours to cover the distance,then:

One of the two buses completes a journey of $300 \, km$ in $7 \frac{1}{2} \, hours$ and the other a journey of $450 \, km$ in $9 \, hours.$ The ratio of their average speed is:

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 $.5$)?

If a train $110 \, m$ long passes a telegraph pole in $3 \, seconds$,then the time taken (in $seconds$) by it to cross a railway platform $165 \, m$ long is:

Two trains measuring $100\, m$ and $80\, m$ respectively,run on parallel tracks. When travelling in opposite directions,they are observed to pass each other in $9\, s$. When they are running in the same direction at the same speeds as before,the faster train passes the other in $18\, s$. Find the speeds of the two trains in $km/h$.

$A$ man standing on a railway platform observes that a train going in one direction takes $4 \,seconds$ to pass him. Another train of the same length going in the opposite direction takes $5 \,seconds$ to pass him. The time taken (in $seconds$) by the two trains to cross each other will be: