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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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