CAT 2020 Quant Question [Slot 2] with Solution 14

Question

Two circular tracks T1 and T2 of radii 100 m and 20 m, respectively touch at a point A. Starting from A at the same time, Ram and Rahim are walking on track T1 and track T2 at speeds 15 km/hr and 5 km/hr respectively. The number of full rounds that Ram will make before he meets Rahim again for the first time is

  1. 4
  2. 3
  3. 2
  4. 5
Option: 2
Solution:

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 \( = \frac{{144\pi }}{{48\pi }} = 3\)

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