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 × 10x = 12x
    Thirteenth number = 850/9 × 1/100 × 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 × 9 = 108

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