CAT (QA) PYQs

Moody takes $30$ seconds to finish riding an escalator if he walks on it at his normal speed in the same direction. He takes $20$ seconds to finish riding the escalator if he walks at twice his normal speed in the same direction. If Moody decides to stand still on the escalator, then the time, in seconds, needed to finish riding the escalator is

Point $P$ lies between points $A$ and $B$ such that the length of $BP$ is thrice that of $AP$ . Car $1$ starts from $A$ and moves towards $B$ . Simultaneously, car $2$ starts from $B$ and moves towards $A$. Car $2$ reaches $P$ one hour after car $1$ reaches $P$. If the speed of car $2$ is half that of car $1$, then the time, in minutes, taken by car $1$ in reaching $P$ from $A$ is

$A$ and $B$ are two railway stations $90 \mathrm{~km}$ apart. A train leaves $A$ at $9:00$ am, heading towards $B$ at a speed of $40 \mathrm{~km} / \mathrm{hr}$. Another train leaves $B$ at $10:30$ am, heading towards $A$ at a speed of $20 \mathrm{~km} / \mathrm{hr}$. The trains meet each other at