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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 250, 240, and 230. Determine the difference between the largest and smallest numbers.
      A 100 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=250×2=500

      x+2y+z=240×2=480

      x+y+2z=230×2=460

      Thus,

      4×(x+y+z)=1440

      x+y+z=360

      Now,

      x=500−360=140

      y=480−360=120

      z=460−360=100

      Desired difference = 140−100=40

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