Question
Aman and Rohan start running simultaneously on a
circular track in opposite directions. Aman runs at a speed of 12 km/h while Rohan runs at 18 km/h. After every 10 minutes, their speeds are halved. If the length of the circular track is 1200 m, how many times will Aman and Rohan meet on the track?Solution
Relative speed of Aman and Rohan = 12 + 18 = 30 km/h. After 10 minutes, their speeds are halved, so their effective speed becomes 15 km/h for the next 10 minutes, and so on. The total distance covered in the first 10 minutes = 30 × (10/60) = 5 km. In the next 10 minutes, the relative speed is halved to 15 km/h, so distance = 15 × (10/60) = 2.5 km. This forms a geometric progression where the total distance can be calculated as: Total distance = 5 + 2.5 + 1.25 + ... Sum = 5 / (1 - 1/2) = 10 km. Since each complete meeting corresponds to 1 lap (1200 m or 1.2 km), the number of meetings is: Number of meetings = 10 × 1000 / 1200 = 8.33 ≈ 8 times. Correct Option: d) 8
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