# 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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