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

Train $T$ leaves station $X$ for station $Y$ at $3 \mathrm{pm}$. Train $S$, traveling at three quarters of the speed of $T$, leaves $Y$ for $X$ at $4 \mathrm{pm}$. The two trains pass each other at a station $Z$, where the distance between $X$ and $Z$ is three-fifths of that between $X$ and $Y$. How many hours does train $T$ take for its journey from $X$ to $Y$ ?

Two persons are walking beside a railway track at respective speeds of $2$ and $4 \mathrm{~km}$ per hour in the same direction. A train came from behind them and crossed them in $90$ and $100$ seconds, respectively. The time, in seconds, taken by the train to cross a stationary object?