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      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?
      A 3 Correct Answer Incorrect Answer
      B 4 Correct Answer Incorrect Answer
      C 5 Correct Answer Incorrect Answer
      D 8 Correct Answer Incorrect Answer

      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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