Question:medium

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

Updated On: Jan 15, 2026
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The Correct Option is B

Solution and Explanation

Step 1: Convert speeds from km/h to m/s

  • Ram's speed = \( \frac{15 \times 1000}{60 \times 60} = \frac{15 \times 5}{18} = \frac{75}{18} \) m/s
  • Rahim's speed = \( \frac{5 \times 1000}{60 \times 60} = \frac{5 \times 5}{18} = \frac{25}{18} \) m/s

Step 2: Determine the circumference of each circular path

  • Ram's path circumference: \( C_R = 2\pi \times 100 = 200\pi \) meters
  • Rahim's path circumference: \( C_H = 2\pi \times 20 = 40\pi \) meters

Step 3: Calculate the time required for one complete round

  • Ram's time per round = \( \frac{200\pi}{\frac{75}{18}} = \frac{200\pi \times 18}{75} = 48\pi \) seconds
  • Rahim's time per round = \( \frac{40\pi}{\frac{25}{18}} = \frac{40\pi \times 18}{25} = 28.8\pi \) seconds

Step 4: Find the Least Common Multiple (LCM) of the two round times

The LCM of \( 48\pi \) and \( 28.8\pi \) is calculated as follows: \[ \text{LCM}(48\pi, 28.8\pi) = 144\pi \text{ seconds} \]

Step 5: Determine the number of rounds Ram completes within the LCM time

The number of rounds Ram completes is: \[ \text{Rounds} = \frac{144\pi}{48\pi} = \boxed{3} \]

Answer:

Ram will meet Rahim after completing 3 full rounds.

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In the dynamic realm of creativity, artists often find themselves at the crossroads between drawing inspiration from diverse cultures and inadvertently crossing into the territory of cultural appropriation. Inspiration is the lifeblood of creativity, driving artists to create works that resonate across borders. In a globalized era of the modern world, artists draw from a vast array of cultural influences. When approached respectfully, inspiration becomes a bridge, fostering understanding and appreciation of cultural diversity. However, the line between inspiration and cultural appropriation can be thin and easily blurred.
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