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      Question

      The ages of 4 members of a family are in the year 2011 are β€˜X’,’X+6’,’X+12’ and β€˜X+18’. After some years Oldest among them was dead then average reduced by 2. After how many years from his death, the average age will same as in 2011?

      A 6 years Correct Answer Incorrect Answer
      B 2 years Correct Answer Incorrect Answer
      C 5 years Correct Answer Incorrect Answer
      D 3 years Correct Answer Incorrect Answer
      E 4 years Correct Answer Incorrect Answer

      Solution

      Average of all in 2011 = {X + (X+6) + (X+12) + (X+18)}/4 = (4X + 36)/4 = X + 9 Let the oldest die after N years, then average of three persons, {X + (X+6) + (X+12) + 3N}/3 = (X+9-2) (3X+18+3N)/3 = X+7 X+6+N = X+7 N = 1 years Let after another M years, their average will be equal to that in 2011. So, (3X+18+3N+3M)/3 = X+9 (3X + 18 + 3x1 + 3M)/3 = X+9 X + 6 +1 +M = X+9 M = 2 years

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