CAT (QA) PYQs

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

$A$ 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

A motorbike leaves point $A$ at $1$ pm and moves towards point $B$ at a uniform speed. A car leaves point $B$ at $2$ pm and moves towards point $A$ at a uniform speed which is double that of the motorbike. They meet at $3:40$ pm at a point which is $168 \mathrm{~km}$ away from $A$ . What is the distance, in km, between $A$ and $B$ ?