CAT (QA) PYQs

Two cars travel the same distance starting at $10:00$ am and $11:00$ am, respectively, on the same day. They reach their common destination at the same point of time. If the first car travelled for at least $6$ hours, then the highest possible value of the percentage by which the speed of the second car could exceed that of the first car is

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?

Vimla starts for office every day at $9$ am and reaches exactly on time if she drives at her usual speed of $40 \mathrm{~km} / \mathrm{hr}$. She is late by $6$ minutes if she drives at $35 \mathrm{~km} / \mathrm{hr}$. One day, she covers two-thirds of her distance to office in onethirds of her usual time to reach office, and then stops for $8$ minutes. The speed, in km/hr, at which she should drive the remaining distance to reach office exactly on time is