$A$ man walks at the rate of $5 \, km/hr$ for $6 \, hours$ and at $4 \, km/hr$ for $12 \, hours$. The average speed of the man (in $km/hr$) is:

$A$ train $300 \text{ m}$ long is running at a speed of $90 \text{ km/h}$. How many seconds will it take to cross a $200 \text{ m}$ long train running in the opposite direction at a speed of $60 \text{ km/h}$?

One of the two buses completes a journey of $300 \, km$ in $7 \frac{1}{2} \, hours$ and the other a journey of $450 \, km$ in $9 \, hours.$ The ratio of their average speed is:

$A$ boy walking at a speed of $10\, km/hr$ reaches his school $15\, minutes$ late. Next time he increases his speed by $2\, km/hr$, but still he is late by $5\, minutes$. Find the distance of his school from his house (in $km$).

$A$ man goes from a place $A$ to $B$ at a speed of $12 \, km/h$ and returns from $B$ to $A$ at a speed of $18 \, km/h$. The average speed for the whole journey is? (in $km/h$)

$A$ 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: