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      Question

      In a race of 300 metres, 'P' defeats 'R' by 45 metres, and

      'R' defeats 'Q' by 30 metres. Find out how many metres 'P' defeats 'Q' by.
      A 95.5 m Correct Answer Incorrect Answer
      B 70.5 m Correct Answer Incorrect Answer
      C 25.5 m Correct Answer Incorrect Answer
      D 36.5 m Correct Answer Incorrect Answer

      Solution

      ATQ,

      Let the time taken by 'P' to finish = t seconds

      Then, distance covered by 'R' in t seconds = 300 - 45 = 255 metres

      So, ratio of speeds of 'P' and 'R' = 300 : 255 = 20 : 17

      Now, R beats Q by 30 metres, so:

      Ratio of speeds of 'R' and 'Q' = 300 : (300 - 30) = 300 : 270 = 10 : 9

      Now, combine:

      Ratio of speeds of P, R, Q = 20×10 : 17×10 : 17×9 = 200 : 170 : 153

      So, when 'P' runs 300 metres, 'Q' runs = 300 × (153/200) = 229.5 metres

      Therefore, 'P' beats 'Q' by 300 - 229.5 = 70.5 metres

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