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      Question

      The sum of the first, second, and

      third numbers is 231. The first and second numbers are in a 3:5 ratio, and the second and third numbers are in a 4:9 ratio. Find the difference between the first and third numbers.
      A 105 Correct Answer Incorrect Answer
      B 72 Correct Answer Incorrect Answer
      C 99 Correct Answer Incorrect Answer
      D 48 Correct Answer Incorrect Answer
      E 84 Correct Answer Incorrect Answer

      Solution

      Let the 1st, 2nd and 3rd number be x, y and z, respectively According to the question, (x:y) = 3:5 and (y:z) = 4:9 Therefore, ratio of x:y:z = 12:20:45 Let the numbers be 12a, 20a and 45a, respectively Therefore, 12a + 20a + 45a = 231 Or, 77a = 231 Or, a = 3 Required difference = (45a – 12a) = 33a = 99 Hence, option c.

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