CAT (QA) PYQs

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

Arvind travels from town $A$ to town $B$, and Surbhi from town B to town $A$, both starting at the same time along the same route. After meeting each other, Arvind takes $6$ hours to reach town $B$ while Surbhi takes $24$ hours to reach town $A$. If Arvind travelled at a speed of $54 \mathrm{~km} / \mathrm{h}$, then the distance, in km, between town $A$ and town $B$ is

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