Two trains are moving in the same direction at $50 \, km/h$ and $30 \, km/h$. The faster train crosses a man in the slower train in $18 \, seconds$. Find the length of the faster train (in $m$).

$A$ car covers a distance of $330 \, km$ in a certain amount of time at a speed of $55 \, km/h$. What is the average speed of a bike that covers a distance of $15 \, km$ less than the car in $1 \, hour$ less than the time taken by the car? (in $km/h$)

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

The fare of a bus is $Rs. X$ for the first five kilometres and $Rs. 13$ per kilometer thereafter. If a passenger pays $Rs. 2402$ for a journey of $187$ kilometres,what is the value of $X$? (in $Rs.$)

Paschim Express left Delhi for Mumbai at $14:30\, \text{hours}$ travelling at a speed of $60\, \text{km/h}$. August Kranti Express left Delhi for Mumbai on the same day at $16:30\, \text{hours}$ travelling at a speed of $80\, \text{km/h}$. How far away from Delhi will the two trains meet (stoppages excluded)? (in $\text{km}$)

$A$ train travels at a speed of $10\, m/s$ and leaves Trivandrum for Nagercoil at $8\, AM$. At what distance from Nagercoil will it meet a train which leaves Nagercoil for Trivandrum at $8.20\, AM$ and travels one-third faster than the former? The distance from Trivandrum to Nagercoil is $68\, km$. (in $km$)