Raj and Prem walk in opposite directions at the rate of $3 \, km/h$ and $2 \, km/h$ respectively. How far will they be from each other after $2 \, hours$? (in $km$)

The speeds of $A$ and $B$ are in the ratio of $3: 4$. $A$ takes $20 \, min$ more than $B$ to reach a destination. Find the time in which $A$ reaches the destination.

$A$ and $B$ run a kilometer and $A$ wins by $25 \, s.$ $A$ and $C$ run a kilometer and $A$ wins by $275 \, m.$ When $B$ and $C$ run the same distance,$B$ wins by $30 \, s.$ The time taken by $A$ to run a kilometer 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 time taken by them is $14 \, hours$. Then $A$'s speed is equal to (in $km/hr$)

Two men $A$ and $B$ walk from $P$ to $Q$ at a distance of $21 \text{ km}$ at speeds of $3 \text{ km/h}$ and $4 \text{ km/h}$ respectively. $B$ reaches $Q$ and returns immediately and meets $A$ at $R$. The distance from $P$ to $R$ is (in $\text{km}$):

The speed of a train going from Nagpur to Allahabad is $100 \text{ km/h}$,while its speed is $150 \text{ km/h}$ when coming back from Allahabad to Nagpur. What is the average speed during the whole journey in $\text{km/h}$?