CAT (QA) PYQs

Ravi is driving at a speed of $40$ km/h on a road. Vijay is $54$ meters behind Ravi and driving in the same direction as Ravi. Ashok is driving along the same road from the opposite direction at a speed of $50$ km/h and is $225$ meters away from Ravi. The speed, in km/h, at which Vijay should drive so that all the three cross each other at the same time, 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

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?