Question
The ages of 4 members of a family are in the year 2011
are ‘X’,’X+6’,’X+12’ and ‘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?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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