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    Question

    The average of 16 numbers is 75. The first six numbers

    and the last five numbers have averages of 90 and 72 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 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 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 = 75 × 16 – 6 × 90 – 5 × 72
    = 1200 – 540 – 360
    = 300
    Or, 100x/3 = 300
    Or, x = 9
    So, ninth number = 12 × 9 = 108

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