Question : Two runners, Sony and Mony, start running on a circular track of length 200 m at speeds of 18 km/h and 24 km/h, respectively, in the same direction. After how much time from the start will they meet again at the starting point?
Option 1: 120 sec
Option 2: 110 sec
Option 3: 100 sec
Option 4: 90 sec
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Correct Answer: 120 sec
Solution : We know, Sony and Mony, running on a circular track in the same direction of length 200 m at speeds of 18 km/h and 24 km/h. Speed of Sony = 18 km/h = 18 × $\frac{5}{18}$ m/s = 5 m/s So, time taken by Sony to complete one lap = $\frac{200}{5}$ sec = 40 sec Speed of Mony = 24 km/h = 24 × $\frac{5}{18}$ m/s = $\frac{20}{3}$ m/s So, time taken by Sony to complete one lap = $\frac{200}{\frac{20}{3}}$ sec = 30 sec Time of meeting at starting track for first time = LCM of time taken by individuals to complete one lap = LCM (40, 30) = 120 sec Hence, the correct answer is 120 sec.
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