Question : In a circular race of 1500 m. Anil and Bilal start from the same point and at the same time with speeds of 36 km/hr and 54 km/hr respectively. When will they meet again for the first time on the track when they are running in the same direction?
Option 1: 300 sec
Option 2: 250 sec
Option 3: 140 sec
Option 4: 320 sec
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Correct Answer: 300 sec
Solution : Speed of Amal = 36 km/hr = 36 × $\frac{5}{18}$ = 10 m/s Speed of Bimal = 54 km/hr = 54 × $\frac{5}{18}$ = 15 m/s Time taken by Amal to complete one round = $\frac{1500}{10}$ = 150 sec Time taken by Bimal to complete one round = $\frac{1500}{15}$ = 100 sec They will meet at the starting point at a time which is the LCM of the timings taken by each of them to complete one full round. i.e., the LCM of 150 and 100 which is 300 sec. Hence, the correct answer is 300 sec.
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