CAT (QA) PYQs

Leaving home at the same time, Amal reaches the office at $10:15 am$ if he travels at $8 km/hr$, and at $9:40 am$ if he travels at $15 km/hr$. Leaving home at 9:10, at what speed, in $km/hr,$ must be travel so as to reach office exactly at $10 am?$

In a $10 \mathrm{~km}$ race. A, B, and C , each running at uniform speed, get the gold, silver, and bronze medals, respectively. If A beats B by $1 \mathrm{~km}$ and B beats C by $1 \mathrm{~km}$, then by how many metres does A beat C?

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?