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    Question

    Three numbers are given such that when the average of

    any two numbers is added to the third number, the resulting sums are 350, 330, and 310. Determine the difference between the largest and smallest numbers.
    A 32 Correct Answer Incorrect Answer
    B 80 Correct Answer Incorrect Answer
    C 42 Correct Answer Incorrect Answer
    D 20 Correct Answer Incorrect Answer
    E None of these Correct Answer Incorrect Answer

    Solution

    ATQ;
    Let the three numbers be x, y, and z.

    So,2x+y+z=350×2=700

    x+2y+z=330×2=660

    x+y+2z=310×2=620
    Thus,

    4×(x+y+z)=1980

    x+y+z=495

    Now,

    x=700−495=205

    y=660−495=165

    z=620−495=125

    Desired difference = 205−125=80

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