CAT (QA) PYQs

Anil, Sunil, and Ravi run along a circular path of length $3 \mathrm{~km}$, starting from the same point at the same time, and going in the clockwise direction. If they run at speeds of $15 \mathrm{~km} / \mathrm{hr}, 10 \mathrm{~km} / \mathrm{hr}$, and $8 \mathrm{~km} / \mathrm{hr}$, respectively, how much distance in km will Ravi have run when Anil and Sunil meet again for the first time at the starting point?

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

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 $B$ ?