Amit started cycling along the boundaries of a square field from corner point $A$. After half an hour,he reached the corner point $C$,diagonally opposite to $A$. If his speed was $8 \, km/h$,what is the area of the field in square $km$?

Two places $P$ and $Q$ are $162 \, km$ apart. $A$ train leaves $P$ for $Q$ and simultaneously another train leaves $Q$ for $P$. They meet at the end of $6 \, hours$. If the former train travels $8 \, km/h$ faster than the other,then the speed of the train from $Q$ is (in $km/h$):

$A$ 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?

The distance of the sun from the earth is $143,400,000 \text{ km}$. Light travels from the sun to the earth in $7 \text{ minutes}$ and $58 \text{ seconds}$. The velocity of light per second is (in $\times 10^5 \text{ km/sec}$):

$A$ 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:

It takes $24 \, s$ for a train travelling at $93 \, km/h$ to cross entirely another train half its length travelling in the opposite direction at $51 \, km/h$. It passes a bridge in $66 \, s$. What is the length of the bridge in meters?