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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

Explanation:

Time taken by Ram to reach the starting point A = $\frac{2 \times π \times 0.1}{15} = \frac{π}{75}$

Time taken by Rahim to reach the starting point A = $\frac{2 \times π \times 0.02}{5} = \frac{π}{125}$

Both of them will meet only at A since they are running in different circles which meet at A.

Both of them will reach the starting point after LCM $[\frac{π}{75}, \frac{π}{125}]$ = $\frac{π}{25}$

∴ Number of rounds completed by Ram when both of them meet again = $\frac{\frac{π}{25}}{\frac{π}{75}}$ = 3

Hence, (a).

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