Problems on Trains

The length of a rectangular plot is $20$metres more than its breadth. If the cost of fencing the plot @ Rs. $26.50$ per metre is Rs. $5300$, what is the length of the plot in metres?

A  $250 \mathrm{m}$ Train is running at the average speed$90 \mathrm{km}/\mathrm{hr}$ . How long will it take to pass a standing man?

A bullock cart has to cover a distance of $120 \mathrm{km}$ in $15 \mathrm{hours}$ . If it covers half of the journey in ${\frac{3}{5}}^{\mathrm{th}}$ time, the speed to cover the remaining distance in the time left has to be:

A train passes a station platform in $36 \mathrm{seconds}$ and a man standing on the platform in $20 \mathrm{seconds}$. If the speed of the train in $54 \raisebox{1ex}{$\mathrm{km}$}\!\left/ \!\raisebox{-1ex}{$\mathrm{hr}$}\right.$, what is the length of the platform?

Answer the question based on the following information:

A fort had provision of food for $150$men for $45$days. After $10$days, $25$men left the fort. The number of days for which the remaining food will last, is:

A thief steals a car at $2.30$pm and drives it at $60$kmph. The theft is discovered at $3$pm and the owner sets off in another car at $75$ kmph when will he overtake the thief ?

Two trains of length of $250 \mathrm{m}$ and $200 \mathrm{m}$ are running in the same direction, if the trains cross each other in $45 \mathrm{seconds}$ and the speed of the first train is $27 \raisebox{1ex}{$\mathrm{km}$}\!\left/ \!\raisebox{-1ex}{$\mathrm{hr}$}\right.$, find speed of the second train.

A man walking at ${\frac{4}{5}}^{th}$th of his original speed reaches his destination in $15$ minutes later than the usual time. Then the usual time is:

During a journey of $80 \mathrm{km}$, a train covers the first $60 \mathrm{km}$ with a speed of $40 \mathrm{km}/\mathrm{hr}$ and completes the remaining distance with a speed of $20 \mathrm{km}/\mathrm{hr}$. What is the average speed of the train during the whole journey$?$

A man in a train notices that he can count $21$telephone posts in one minute. If they are known to be $50$metres apart, at what speed is the train travelling?

Two trains, $125 \mathrm{metres}$ and $115 \mathrm{metres}$ in length, are running towards each other on parallel lines, one at the rate of $33 \mathrm{kmph}$ and the other at $39 \mathrm{kmph}$. How much time (in $\sec$) will they take to pass each other from the moment they meet?

A boat covers a distance of $24$km in down stream in $4$hours while it covers the same distance in upstream in $6$hours. What is the speed of boat in still water?

A man travels on a scooter from $\mathrm{A}$ to $\mathrm{B}$ at a speed of $30 \mathrm{km}/\mathrm{hr}$ and returns from  $\mathrm{B}$ to $\mathrm{A}$ at $20 \mathrm{km}/\mathrm{hr}$. The total journey was performed by him in $10 \mathrm{hours}$. Find the distance from  $\mathrm{A}$ to $\mathrm{B}$.

A Kinetic Honda covers a distance of $140 \mathrm{km}$ in $2 \mathrm{hours} \mathrm{and} 20 \mathrm{minutes}$ while a car covers the same distance in $1 \mathrm{hour} \mathrm{and} 40 \mathrm{minutes}$. What is the ratio of their speeds?

Answer the question based on the following information:

A car travels a distance of $75 \mathrm{km}$ at the speed of$25 \raisebox{1ex}{$\mathrm{km}$}\!\left/ \!\raisebox{-1ex}{$\mathrm{hr}$}\right.$. It covers the next $25 \mathrm{km}$ of its journey at the speed of $5 \raisebox{1ex}{$\mathrm{km}$}\!\left/ \!\raisebox{-1ex}{$\mathrm{hr}$}\right.$ and the last $50 \mathrm{km}$ of its journey at the speed of $25 \raisebox{1ex}{$\mathrm{km}$}\!\left/ \!\raisebox{-1ex}{$\mathrm{hr}$}\right.$. What is the average speed of the car?

A thief is noticed by a policeman from a distance of $200$m. The thief starts running and the policeman chases him. The thief and the policeman run at the rate of $10$km and $11$km per hour respectively. What is the distance between them after $6$minutes?

Answer the question based on the following information:

If a car travels $20 \mathrm{km}$ in $2 \mathrm{hours}$ and another $10 \mathrm{km}$ in $3 \mathrm{hours}$, the average speed of the car is: