If the length of the train is $700 \, m$ and the length of the platform is $500 \, m$,find the time taken by the train moving at $54 \, km/h$ to cross the platform (in $sec$).

$A$ truck covers $224 \ km$ in $4 \ hours$. The average speed of a bike is $\frac{1}{4}$ of the average speed of the truck. How much distance will the bike cover in $7 \ hours$? (in $km$)

$A$ man driving at $\frac{3}{4}$ of his original speed reaches his destination $20 \text{ minutes}$ later than the usual time. Then the usual time is (in $\text{minutes}$)

$A$ 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 leaves the station $1 \, hr$ before the scheduled time. The driver decreases its speed by $4 \, km/hr$. At the next station $120 \, km$ away,the train reaches on time. Find the original speed of the train in $km/hr$.

$P$ and $Q$ are $27 \, km$ apart. Two trains with speeds of $24 \, km/h$ and $18 \, km/h$ respectively start simultaneously from $P$ and $Q$ and travel in the same direction. They meet at a point $R$ beyond $Q$. The distance $QR$ is (in $km$):