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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 450, 420, and 400. Determine the difference between the largest and smallest numbers.
    A 100 Correct Answer Incorrect Answer
    B 80 Correct Answer Incorrect Answer
    C 62 Correct Answer Incorrect Answer
    D 90 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=450×2=900

    x+2y+z=420×2=840

    x+y+2z=400×2=800

    Thus,

    4×(x+y+z)=2640

    x+y+z=660

    Now,

    x=900−660=240

    y=840−660=180

    z=800−660=140

    Desired difference = 240−140=100

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