CAT (QA) PYQs

Ankita walks from A to C through B, and runs back through the same route at a speed that is 40% more than her walking speed. She takes exactly 3 hours 30 minutes to walk from B to C as well as to run from B to A. The total time, in minutes, she would take to walk from A to B and run from B to C, is

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