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      Question

      The average of 19 numbers is 80. The first eight

      numbers have an average of 100, and the last six numbers have an average of 70. The twelfth number exceeds the eleventh number by 20%, and the thirteenth number is reduced by (50/9)% from the twelfth number. Determine the value of the twelfth 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 eleventh number is 10x
      So, twelfth number = 1.20 Ă— 10x = 12x
      Thirteenth number = 850/9 Ă— 1/100 Ă— 12x = 34x/3
      So, 10x + 12x + 34x/3 = 80 × 19 – 8 × 100 – 6 × 70
      = 1520 – 800 – 420
      = 300
      Or, 100x/3 = 300
      Or, x = 9
      So, twelfth number = 12 Ă— 9 = 108

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