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 man leaves his home and walks at a speed of $12$ km per hour, reaching the railway station $10$ minutes after the train had departed. If instead he had walked at a speed of $15$ km per hour, he would have reached the station $10$ minutes before the train's departure. The distance (in km) from his home to the railway station is

$A$ and $B$ are two points on a straight line. Ram runs from $A$ to $B$ while Rahim runs from $B$ to $A$. After crossing each other, Ram and Rahim reach their destinations in one minute and four minutes, respectively. If they start at the same time, then the ratio of Ram's speed to Rahim's speed is