R. S. Aggarwal Solutions for Chapter: Problems on Trains, Exercise 1: EXERCISE 18A

A train of length $150 \mathrm{m}$, takes $10$ seconds to pass over another train $100 \mathrm{m}$ long coming from the opposite direction. If the speed of first train be $30 \mathrm{km}/\mathrm{hr}$, the speed of the second train is ______.

Two trains running in opposite directions cross a man standing on the platform in $27$ seconds and $17$ seconds respectively and they cross each other in $23$ seconds. The ratio of their speeds is______.

A train travelling at $54 \mathrm{km}/\mathrm{hr}$ crosses another train having half of its length and travelling in opposite direction at $81 \mathrm{km}/\mathrm{hr}$ in $12$ seconds. If it passes a railway platform in $1\frac{1}{2}$ minutes, the length of the platform is_______.

Two trains of equal length are running on parallel lines in the same direction at the rate of $92 \mathrm{km}/\mathrm{hr}$ and $72 \mathrm{km}/\mathrm{hr}$ respectively. The faster train passes the slower train in $54$ seconds. The length of each train is_____.

A train $270 \mathrm{m}$ long is moving at a speed of $25 \mathrm{km}/\mathrm{hr}$. It will cross a man coming from the opposite direction at $2 \mathrm{km}/\mathrm{hr}$ in _____.

A train $\mathrm{X}$ starts from city $\mathrm{A}$ at $5 \mathrm{p}.\mathrm{m}.$ and reaches city $\mathrm{B}$ at $6 \mathrm{p}.\mathrm{m}$. while another train $\mathrm{Y}$ starts from city $\mathrm{B}$ at $5 \mathrm{p}.\mathrm{m}.$ and reaches city $\mathrm{A}$ at $6.30 \mathrm{p}.\mathrm{m}.$ The two trains will cross each other at_______.

Two trains, one from station $\mathrm{A}$ to station $\mathrm{B}$ and the other from $\mathrm{B}$ to $\mathrm{A}$ start simultaneously. After meeting, the trains reach their destinations after $16 \mathrm{hours}$ and $9 \mathrm{hours}$ respectively. The ratio of their speeds is_____.

A train is running at $40 \mathrm{km}/\mathrm{hr}$. A man is going in the same direction parallel to the train at $25 \mathrm{km}/\mathrm{hr}$. If the train crosses the man in $48$ seconds, the length of the train is_______.