MAT Exam 2022 Paper

Concept:The two tracks touch only at point $A$.So Ram and Rahim can meet again only when both reach $A$ at the same time after completing whole numbers of rounds.Explanation:Radius of track $T_1$ is $100\,m$ and radius of track $T_2$ is $20\,m$.Circumference of $T_1 = 2\pi(100) = 200\pi\,m$.Circumference of $T_2 = 2\pi(20) = 40\pi\,m$.Therefore, ratio of circumferences $= 200\pi : 40\pi = 5:1$.Speeds are $15\,km/hr$ and $5\,km/hr$, so speed ratio $= 15:5 = 3:1$.Time for one round $= \dfrac{\text{circumference}}{\text{speed}}$.Hence, time per round ratio:$\dfrac{5}{3} : \dfrac{1}{1} = 5:3$.So Ram takes $5$ units of time per round while Rahim takes $3$ units.Let Ram make $n$ rounds and Rahim make $m$ rounds before meeting again.Meeting condition: $5n = 3m$.Smallest whole-number solution is $n = 3$, $m = 5$.Thus Ram completes $3$ full rounds, and Rahim completes $5$ full rounds at their first meeting after start.Answer:Ram makes $\boxed{3}$ full rounds before meeting Rahim again for the first time.Correct option: B.