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?

The distance from $B$ to $C$ is thrice that from $A$ to $B$. Two trains travel from $A$ to $C$ via $B$. The speed of train $2$ is double that of train $1$ while traveling from $A$ to $B$ and their speeds are interchanged while traveling from $B$ to $C$. The ratio of the time taken by train $1$ to that taken by train $2$ in travelling from $A$ to $C$ is

Moody takes $30$ seconds to finish riding an escalator if he walks on it at his normal speed in the same direction. He takes $20$ seconds to finish riding the escalator if he walks at twice his normal speed in the same direction. If Moody decides to stand still on the escalator, then the time, in seconds, needed to finish riding the escalator is