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      Question

      In a 500-metre race, 'M' beats 'O' by 100 metres, and 'O'

      beats 'N' by 75 metres. Find by how much distance 'M' beats 'N'.
      A 160 m Correct Answer Incorrect Answer
      B 115 m Correct Answer Incorrect Answer
      C 125 m Correct Answer Incorrect Answer
      D 136 m Correct Answer Incorrect Answer

      Solution

      ATQ,

      Let time taken by 'M' to complete the race = t seconds

      Then, 'O' covers = 500 - 100 = 400 metres

      So, ratio of speeds of 'M' and 'O' = 500 : 400 = 5 : 4

      'O' beats 'N' by 75 metres:

      So, speed ratio of 'O' and 'N' = 500 : (500 - 75) = 500 : 425 = 20 : 17

      Combining:

      M : O : N = 5×20 : 4×20 : 4×17 = 100 : 80 : 68

      When 'M' runs 500 metres, 'N' runs = 500 × (68/100) = 340 metres

      Hence, 'M' beats 'N' by 500 - 340 = 160 metres

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