Speed, Time and Distance — CDS Elementary Mathematics PYQs

A train $P$ starts from station $X$ for station $Y$ and another train $Q$ starts from station $Y$ for station $X$ at the same time. After passing each other, $P$ takes 4 hours to reach $Y$ and $Q$ takes 1 hour to reach $X$. If the average speed of $P$ is 60 km/h, then what is the average speed of $Q$?

Without stoppages, a train travels at an average speed of 60 km/h and with stoppages it covers the same distance at an average speed of 48 km/h. How many minutes per hour does the train stop?

A person goes downstream at $x$ km/h and upstream at $y$ km/h by the same boat. What is the ratio of speed of boat in still water to speed of water?

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?