CAT (QA) PYQs

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

Point $P$ lies between points $A$ and $B$ such that the length of $BP$ is thrice that of $AP$ . Car $1$ starts from $A$ and moves towards $B$ . Simultaneously, car $2$ starts from $B$ and moves towards $A$. Car $2$ reaches $P$ one hour after car $1$ reaches $P$. If the speed of car $2$ is half that of car $1$, then the time, in minutes, taken by car $1$ in reaching $P$ from $A$ is

Two trains cross each other in $14$ seconds when running in opposite directions along parallel tracks. The faster train is $160$ m long and crosses a lamp post in $12$ seconds. If the speed of the other train is $6$ km/hr less than the faster one, its length, in m, is