CAT (QA) PYQs

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?

Points $A$ and $B$ are $150 \mathrm{~km}$ apart. Cars $1$ and $2$ travel from $A$ to $B$, but car $2$ starts from $A$ when car $1$ is already $20 \mathrm{~km}$ away from $A$. Each car travels at a speed of $100 \mathrm{kmph}$ for the first $50 \mathrm{~km}$, at $50 \mathrm{kmph}$ for the next $50 \mathrm{~km}$, and at $25 \mathrm{kmph}$ for the last $50 \mathrm{~km}$. The distance, in km, between car $2$ and $B$ when car $1$ reaches $B$ is

Two trains $A$ and $B$ were moving in opposite directions, their speeds being in the ratio $5: 3$. The front end of $A$ crossed the rear end of $B$ $46$ seconds after the front ends of the trains had crossed each other. It took another $69$ seconds for the rear ends of the trains to cross each other. The ratio of length of train $A$ to that of train $B$ is