CAT 2020 Quant Question [Slot 2] with Solution 14

Time taken by each of them to complete one round

\( = \frac{{{\text{Circumference of the circle}}}}{{{\text{speed}}}}\)

Time taken for Ram to cover one round \( = \frac{{2\pi  \times 100}}{{15 \times 5/18}} = 48\pi \)

Time taken for Rahim to cover one round \( = \frac{{2\pi  \times 20}}{{5 \times 5/18}} = 28.8\pi \)

Time taken by Ram and Rahim meet each other for the first time \( = LCM\) of \(48\pi \) and \(28.8\pi  = 144\pi \)

\(\therefore \) Number of rounds made by Ram before he meets Rahim for the first time \( = \frac{{144\pi }}{{48\pi }} = 3\)