$A$ person travels from $P$ to $Q$ at a speed of $40 \, km/hr$ and returns by increasing his speed by $50 \%$. What is his average speed for both the trips? (in $km/hr$)

$A$ train crosses a platform in $30 \, s$ travelling with a speed of $60 \, km/h$. If the length of the train is $200 \, m$, then the length of the platform is (in $m$):

$A$ train running at $25 \, km/hr$ takes $18 \, seconds$ to pass a platform. Next,it takes $12 \, seconds$ to pass a man walking at $5 \, km/hr$ in the opposite direction. Find the sum of the length of the train and that of the platform (in $m$).

Rakesh sets out to cycle from Delhi to Mathura and at the same time Suresh starts from Mathura to Delhi. After passing each other,they complete their journeys in $9$ and $16 \, \text{hours}$,respectively. At what speed does Suresh cycle if Rakesh cycles at $16 \, \text{km/h}$?

$A$ 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:

$A$ man starts running from point $P$ at $11:00$ $a.m.$ with a speed of $10 \, km/hr$. He runs for $2 \, hours$ and then takes a $1 \, hour$ rest. He continues this pattern until he is caught by another man who starts at $2:00 \, p.m.$ from point $P$ and runs non-stop at a speed of $15 \, km/hr$ toward the first man. At what time (in $p.m.$) will the first man be caught?