CAT (QA) PYQs

A cyclist leaves $A$ at $10$ am and reaches $B$ at $11$ am. Starting from $10:01$ am, every minute a motor cycle leaves $A$ and moves towards $B$. Forty-five such motor cycles reach $B$ by $11$ am. All motor cycles have the same speed. If the cyclist had doubled his speed, how many motor cycles would have reached $B$ by the time the cyclist reached $B$?

Trains A and B start traveling at the same time towards each other with constant speeds from stations X and Y, respectively. Train A reaches station Y in $10$ minutes while train B takes $9$ minutes to reach station X after meeting train A. Then the total time taken, in minutes, by train $B$ to travel from station $Y$ to station $X$ is

Points $A, P, Q$ and $B$ lie on the same line such that $P, Q$ and $B$ are, respectively, $100 \mathrm{~km}, 200 \mathrm{~km}$ and $300 \mathrm{~km}$ away from $A$. Cars $1$ and $2$ leave $A$ at the same time and move towards $B.$ Simultaneously, car $3$ leaves $B$ and moves towards $A$. Car $3$ meets car $1$ at $Q$, and car $2$ at $P$. If each car is moving in uniform speed then the ratio of the speed of car $2$ to that of car $1$ is