NMOS 2010 Q16

Q16. There are five members in John’s family: Father, Mother, John, elder sister Helen, and younger sister Lucy. Just before Lucy was born , the average age of the family was 19 years old, and the age of John’s father is the same as the sum of the age of the rest of the family. Two years ago, the average age of the family was 35.2 years old, and the age of John’s mother was eight years more than the sum of the ages of John and Lucy. The current average age of the family, excluding Helen, is 39.5 years old. Find the present age of John.


F, M, H, J, L

L = 0, F + M + J + H = 19 x 4 = 76


F = M + J + H = 76 / 2 = 38


2 years ago, F + M + J + H + L = 35.2 x 5 = 176


M = J + L + 8



Now, F + M + H + J + L = 176 + 5 x 2 = 186


M = J + L + 8 – 2 = J + L + 6



186 – 76 = 110


110 / 5 = 22 years – L



F = 38 + 22 = 60


F + M + J + L = 39.5 x 4 = 158




M + J = 158 – 60 – 22 = 76


M = J + 22 + 6 = J + 28



J = (76 – 28)/2 = 24 years old