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

• A. 4
• B. 3
• C. 2
• D. 5

Answer 1

Answer: (B)

3

Answer 2

The correct answer is (B): $3$

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 = $\frac{2π×100}{\frac{15×5}{18}} = 48π$

Time taken for Rahim to cover one round = $\frac{2π×20}{\frac{5×5}{18}} = 28.8π$

Time taken by Ram and Rahim meet each other for the first time = LCM of $48π$ and $28.8π$ = $144π$

$∴$ Number of rounds made by Ram before he meets Rahim for the first time = $\frac{144\pi}{48π} = 3$