CAT (QA) PYQs

$A$ 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

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 $B$ ?

Two ships meet mid-ocean, and then, one ship goes south and the other ship goes west, both travelling at constant speeds. Two hours later, they are $60 \mathrm{~km}$ apart. If the speed of one of the ships is $6 \mathrm{~km}$ per hour more than the other one, then the speed, in km per hour, of the slower ship is