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    Question

    The average of 18 numbers is 70. The first eight

    numbers have an average of 90, and the last five numbers have an average of 48. The eleventh number exceeds the tenth number by 20%, and the twelfth number is reduced by (50/9)% from the eleventh number. Determine the value of the eleventh 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 tenth number is 10x
    So, eleventh number = 1.20 × 10x = 12x
    Twelfth number = 850/9 × 1/100 × 12x = 34x/3
    So, 10x + 12x + 34x/3
    = 70 × 18 – 8 × 90 – 5 × 48
    = 1260 – 720 – 240
    = 300
    Or, 100x/3 = 300
    Or, x = 9
    So, eleventh number = 12 × 9 = 108

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