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:

$A$ train $50\, m$ long passes a platform $100\, m$ long in $10\, s$. The speed of the train in $m/s$ is:

$A$ train running at a speed of $60\, km/h$ crosses a platform double its length in $32.4\, seconds.$ What is the length of the platform? (in $m$)

Two cars $P$ and $Q$ start at the same time from $A$ and $B$ which are $120 \, km$ apart. If the two cars travel in opposite directions,they meet after $1 \, hour$,and if they travel in the same direction (from $A$ towards $B$),then $P$ meets $Q$ after $6 \, hours$. What is the speed of car $P$ (in $km/hr$)?

$A$ student goes to school at the rate of $2 \frac{1}{2} \text{ km/h}$ and reaches $6 \text{ min}$ late. If he travels at the speed of $3 \text{ km/h}$,he is $10 \text{ min}$ early. The distance (in $\text{km}$) between the school and his house is:

$A$ is faster than $B$. $A$ and $B$ each walk $24 \, km$. The sum of their speeds is $7 \, km/hr$ and the sum of the times taken by them is $14 \, hours$. Then $A$'s speed is equal to (in $km/hr$):