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      Question

      The average of 15 numbers is 84. The first seven numbers

      and the last five numbers have averages of 92.5 and 72.5, respectively. The ninth number exceeds the eighth number by 20%, and the tenth number is reduced by (50/9)% from the ninth number. Determine the value of the ninth number.
      A 90 Correct Answer Incorrect Answer
      B 80 Correct Answer Incorrect Answer
      C 85 Correct Answer Incorrect Answer
      D 75 Correct Answer Incorrect Answer
      E 115 Correct Answer Incorrect Answer

      Solution

      Let eighth number is 10x So, ninth number = 1.20 × 10x = 12x Tenth number = 850/9 × 1/100 × 12x = 34x/3 So, 10x + 12x + 34x/3 = 84 × 15 – 7 × 92.5 – 5 × 72.5 = 250 Or, 100x/3 = 250 Or, x = 7.5 So, ninth number = 12 × 7.5 = 90

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