CAT (QA) PYQs

Two cars travel from different locations at constant speeds. To meet each other after starting at the same time, they take $1.5$ hours if they travel towards each other, but $10.5$ hours if they travel in the same direction. If the speed of the slower car is $60$ km/hr, then the distance traveled, in km, by the slower car when it meets the other car while traveling towards each other, is

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

Points $A, P, Q$ and $B$ lie on the same line such that $P, Q$ and $B$ are, respectively, $100 \mathrm{~km}, 200 \mathrm{~km}$ and $300 \mathrm{~km}$ away from $A$. Cars $1$ and $2$ leave $A$ at the same time and move towards $B.$ Simultaneously, car $3$ leaves $B$ and moves towards $A$. Car $3$ meets car $1$ at $Q$, and car $2$ at $P$. If each car is moving in uniform speed then the ratio of the speed of car $2$ to that of car $1$ is