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
- 4
- 3
- 2
- 5
The Correct Option is B
Approach Solution - 1
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 = \(\frac{144\pi}{48π} = 3\)
Approach Solution -2
To complete one round Ram takes \(\frac {100\ m}{15\ km/h}\) and Rahim takes \(\frac {20\ m}{5\ km/h}\).
L.C.M of \(\frac {100\ m}{15\ km/h}\), \(\frac {20\ m}{5\ km/h}\)
\(=\frac {100\ m}{5\ km/h}\)
\(=20\ m/kmph\)
So, they meet for the first time after \(20\ m/kmph\).
Distance traveled by Ram,
\(=20\ m/kmph \times 15\ kmph\)
\(=300\ m\)
The number of full rounds,
\(=\frac {300}{100}\)
= \(3\) rounds
So, the correct option is (B): \(3\)
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