Speed, Time and Distance — CDS Elementary Mathematics PYQs

Travelling at $\frac{3}{5}$th of his usual speed, a man is late by 20 minutes. What is the usual time if he travels with his usual speed?

A train of certain length takes time $t$ to pass completely through a station of length $x$. The same train with same speed takes time $2t$ to pass completely through another station of length $y$. What is the time taken by the train to pass completely through a station of length $(x+y)$?

Two trains $X$ and $Y$ are travelling in the same direction at 100 km/hr and 60 km/hr respectively. Train $X$ crosses a man in train $Y$ in 9 seconds. What is the length of train $X$?

Two persons $X$ and $Y$ leave place $P$ for place $Q$ at 7:00 a.m. and 7:10 a.m. respectively along the same path. $X$ walks at a speed of 4.8 km/hr and $Y$ walks at a speed of 6 km/hr. How many kilometres from place $P$ will $X$ meet $Y$?

The speeds of four cars are $2u$, $3u$, $4u$ and $xu$ and the time taken by them to cover the same distance is $xt$, $4t$, $3t$ and $2t$ respectively, where $x$, $u$, $t$ are real numbers. What is the value of $x$?

Two trains $A$ and $B$ leave Delhi for Hyderabad at 7:00 a.m. and 7:50 a.m. on the same day and travel at 80 kmph and 100 kmph respectively. After how many kilometers from Delhi will the two trains be together?

Consider the following for the next three (03) items that follow:
Two trains $A$ and $B$ started from stations $P$ and $Q$ respectively towards each other. Train $A$ started at 7 p.m. at a speed of 60 km/hr and train $B$ started at 4 a.m. (next day) at a speed of 90 km/hr. The distance between $P$ and $Q$ is 800 km.

How far from station $Q$ will the two trains meet?

Consider the following for the next three (03) items that follow:
Two trains $A$ and $B$ started from stations $P$ and $Q$ respectively towards each other. Train $A$ started at 7 p.m. at a speed of 60 km/hr and train $B$ started at 4 a.m. (next day) at a speed of 90 km/hr. The distance between $P$ and $Q$ is 800 km.

At what time will the two trains meet?

Consider the following for the next three (03) items that follow:
Two trains $A$ and $B$ started from stations $P$ and $Q$ respectively towards each other. Train $A$ started at 7 p.m. at a speed of 60 km/hr and train $B$ started at 4 a.m. (next day) at a speed of 90 km/hr. The distance between $P$ and $Q$ is 800 km.

If the lengths of the two trains $A$ and $B$ are 400 m and 500 m respectively, then what is the time taken by them to cross each other?

Train X crosses a man standing on the platform in 24 seconds and train Y crosses a man standing on the platform in 18 seconds. They cross each other while running in opposite directions in 20 seconds. What is the ratio of speed of X to speed of Y?