$A$ person goes from point $A$ to $B$ with a speed of $55 \text{ km/hr}$ and returns with a speed of $65 \text{ km/hr}$. What is the average speed (in $\text{km/hr}$) of the person while going and coming back from $A$ to $B$?

$A$ man standing on a railway platform observes that a train going in one direction takes $4 \,seconds$ to pass him. Another train of the same length going in the opposite direction takes $5 \,seconds$ to pass him. The time taken (in $seconds$) by the two trains to cross each other will be:

How many seconds will a $500 \, m$ long train take to cross a man walking with a speed of $3 \, km/h$ in the direction of the moving train, if the speed of the train is $63 \, km/h$?

$A$ 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:

If a $110 \, m$ long train passes a man walking at a speed of $6 \, km/h$ against it in $6 \, s$,it will pass another man walking at the same speed in the same direction in how many seconds?

$A$ train takes $18 \, s$ to pass completely through a station $162 \, m$ long and $15 \, s$ through another station $120 \, m$ long. The length of the train (in $m$) is: