Question : A, B, and C run simultaneously, starting from a point, around a circular track of length 1200 m, at respective speeds of 2 m/s, 4 m/s, and 6 m/s. A and B run in the same direction, while C runs in the opposite direction to the other two. After how much time will they meet for the first time?
Option 1: 10 minutes
Option 2: 9 minutes
Option 3: 12 minutes
Option 4: 11 minutes
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Correct Answer: 10 minutes
Solution : Circular Track length = 1200 m Speed of A = 2 m/s Speed of B = 4 m/s Speed of C = 6 m/s The relative speed of A and B = 4 – 2 = 6 m/s The relative speed of A and C = 2 + 6 = 8 m/s A and B will meet on the track after every = $\frac{1200}{2}$ = 600 s A and C will meet on the track after every = $\frac{1200}{8}$ = 150 s Thus, A, B, and C will meet together for the first time on the track after = LCM (600, 150) = 600 seconds $\therefore$ They will meet for the first time after = $\frac{600}{60}$ = 10 min Hence the correct answer is 10 minutes.
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