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      Question

      The average of 17 numbers is 80. The first seven

      numbers have an average of 100, and the last five numbers have an average of 72. The tenth number exceeds the ninth number by 20%, and the eleventh number is reduced by (50/9)% from the tenth number. Determine the value of the tenth number.
      A 84 Correct Answer Incorrect Answer
      B 96 Correct Answer Incorrect Answer
      C 108 Correct Answer Incorrect Answer
      D 120 Correct Answer Incorrect Answer
      E 132 Correct Answer Incorrect Answer

      Solution

      Let ninth number is 10x
      So, tenth number = 1.20 × 10x = 12x
      Eleventh number = 850/9 × 1/100 × 12x = 34x/3
      So, 10x + 12x + 34x/3 = 80 × 17 – 7 × 100 – 5 × 72
      = 1360 – 700 – 360
      = 300
      Or, 100x/3 = 300
      Or, x = 9
      So, tenth number = 12 × 9 = 108

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