$A$ boy started from his house by bicycle at $10:00 \, am$ at a speed of $12 \, km/h$. His elder brother started after $1 \, hour \, 15 \, minutes$ by scooter along the same path and caught him at $1:30 \, pm$. The speed of the scooter was (in $km/h$):

$A$ 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:

If a train,with a speed of $60\, km/hr$,crosses a pole in $30\, seconds$,the length of the train (in $meters$) is

Two trains started at the same time,one from $A$ to $B$ and the other from $B$ to $A$. If they arrived at $B$ and $A$ respectively $4 \ hours$ and $9 \ hours$ after they passed each other,the ratio of the speeds of the two trains was:

$A$ train $180 \, m$ long is running at a speed of $90 \, km/h$. How long will it take to pass a post? (in $sec$)

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 $km/h$.