CAT (QA) PYQs

A boat takes $2$ hours to travel downstream a river from port A to port B , and $3$ hours to return to port A . Another boat takes a total of $6$ hours to travel from port $B$ to port $A$ and return to port $B$. If the speeds of the boats and the river are constant, then the time, in hours, taken by the slower boat to travel from port $A$ to port $B$ is

Two ants $A$ and $B$ start from a point $P$ on a circle at the same time, with $A$ moving clock-wise and $B$ moving anti-clockwise. They meet for the first time at $10:00$ am when $A$ has covered $60\%$ of the track. If $A$ returns to $P$ at $10:12$ am, then $B$ returns to $P$ at

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