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    The average of X and Y is 40, that of Y and Z is 38, and that of Z and X is 42. Find the average of X, Y and Z.
    Question

    The average of X and Y is 40, that of Y and Z is 38, and that of Z and X is 42. Find the average of X, Y and Z.

    A.

    120

    B.

    40

    C.

    38

    D.

    42

    Correct option is B

    Given:

    Average of X and Y = 40

    Average of Y and Z = 38

    Average of Z and X = 42

    Formula Used:

    Average of two numbers =Sum of the two numbers2=\dfrac{\text{Sum of the two numbers}}{2}​​

    Solution:

    From the given information:

    X+Y2=40\dfrac{X + Y}{2} = 40

    X + Y = 80

    Y+Z2=\dfrac{Y + Z}{2} = ​ 38

    Y + Z = 76

    Z+X2=42\dfrac{Z + X}{2} = 42

    Z + X = 84

    Now, we add all three equations:

    (X + Y) + (Y + Z) + (Z + X) = 80 + 76 + 84

    2X + 2Y + 2Z = 240

    X + Y + Z =2402 \dfrac{240}{2} ​= 120

    Average of X, Y, and Z =X+Y+Z3=1203=40= \dfrac{X + Y + Z}{3} = \dfrac{120}{3} = 40

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