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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 190, 185, and 180. Determine the difference between the largest and smallest numbers.
    A 20 Correct Answer Incorrect Answer
    B 80 Correct Answer Incorrect Answer
    C 40 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=190×2=380

    x+2y+z=185×2=370

    x+y+2z=180×2=360

    Thus,4×(x+y+z)=1110

    x+y+z=277.5

    Now,

    x=380−277.5=102.5

    y=370−277.5=92.5

    z=360−277.5=82.5

    Desired difference = 102.5−82.5=20

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