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    The average of eight numbers is 20. The average of five of these numbers is 13. The average of the remaining three numbers is
    Question

    The average of eight numbers is 20. The average of five of these numbers is 13. The average of the remaining three numbers is

    A.

    32.67

    B.

    30.67

    C.

    33.67

    D.

    31.67

    Correct option is D

    Given:

    Average of 8 numbers = 20

    Average of 5 of these numbers = 13

    Formula Used:

    Average = Sum of numbersNumber of numbers\frac{\text{Sum of numbers}}{\text{Number of numbers}}​​

    Solution:

    Sum of 8 numbers: 8 ×\times​ 20 = 160

    Sum of 5 numbers: 5×\times13 = 65

    Sum of remaining 3 numbers: 160 - 65 = 95

    Average of remaining 3 numbers: 953\frac{95 }{ 3 }​= 31.67 (approximately)

    Alternate Method:

    Let 'x' be the average of the remaining 3 numbers.

    The overall average of 8 numbers is the weighted average of the two groups (5 numbers and 3 numbers).

    So, (5×13+3×x)8=20\frac{(5 \times 13 + 3 \times x) }{ 8} = 20​​

    65 + 3x = 160

    3x = 95

    x = 953\frac{95}{3}​ or approximately 31.67

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