CAT (QA) PYQs

$A$ 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

Anil, Sunil, and Ravi run along a circular path of length $3 \mathrm{~km}$, starting from the same point at the same time, and going in the clockwise direction. If they run at speeds of $15 \mathrm{~km} / \mathrm{hr}, 10 \mathrm{~km} / \mathrm{hr}$, and $8 \mathrm{~km} / \mathrm{hr}$, respectively, how much distance in km will Ravi have run when Anil and Sunil meet again for the first time at the starting point?

Two runners, Alice and Bob, are racing on two different circular tracks, $T1$ and $T2$, with radii $60 \mathrm{\ m}$ and $40 \mathrm{\ m}$ respectively. They both start from point $P$ at the same moment. Alice runs on track $T1$ at a constant speed of $12 \mathrm{\ km} / \mathrm{hr}$ and Bob runs on track $T2$ at a constant speed of $8 \mathrm{\ km} / \mathrm{hr}$. After how many full rounds of Alice does she meet Bob again for the first time since the race started?