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    Question

    The average of 30 numbers is 72. If the average of the

    first 12 numbers is 60 and the average of the last 19 numbers is 80, find the 12th number.
    A 60 Correct Answer Incorrect Answer
    B 55 Correct Answer Incorrect Answer
    C 80 Correct Answer Incorrect Answer
    D 45 Correct Answer Incorrect Answer

    Solution

    ATQ,

    Sum of all 30 numbers = 30 × 72 = 2160

    Let the 12th number be ‘x’

    Sum of first 12 numbers = 12 × 60 = 720

    Sum of last 19 numbers = 19 × 80 = 1520

    Now, 12th number is included in both groups:

    720 + 1520 - x = 2160

    => 2240 - x = 2160

    => x = 2240 - 2160

    => x = 80

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