The average age of husband, wife and their child 3 years ago = 27 years
Total age of husband, wife and their child 3 years ago = 27 × 3 = 81 years
The average age of wife and the child 5 years ago = 20 years
Total age of wife and child five years ago was 20× 2 = 40 years
? Total age of wife and child 3 years ago
= 40 + (2 × 2)
= 40 + 4 = 44 years
? Age of husband three years ago = Total age of husband, wife and their child 3 years ago - Total age of wife and child 3 years ago
Age of husband three years ago = 81 ? 44 = 37 years
Therefore, the present age of husband = 37 + 3 = 40 years
Suppose that son's age before 4 years = P
Present age of the son = P + 4
At son's birth father's age = 3(P + 4) = 3P + 12
The father's present age = (3P +12) + (P + 4) = 48
? 4P = 48 years ? 16 = 32
? P = 8 years
Therefore, 4 years ago the boy was = 12 ? 4 = 8 years
Suppose the present age of son = P years
The present age of father = Q years
P + Q = 70 ...(i)
According to question, 2(P + 10) = Q + 10
? 2P + 20 = Q + 10
? 2P ? Q = ?10 ....(ii)
From equations (i) and (ii) , we get
3P = 70 ? 10 = 60 ? P = 20 years
? Q = 70 ? 20 = 50 years
Suppose present age of son = P years
Present age of father = 52 years
According to question,
Father's age at son's birth = son's present age
? 52 ? P = P
P + P = 52 years
? 2P = 52
? P = 26 years
Son's age 8 years back = present age of son - 8 years = 26 ? 8 = 18 years
Age of man at the birth of first son = 31 years
The age of wife at the birth of her son = 26 ? 7 = 19 years
Required difference = Age of man at the birth of first son - The age of wife at the birth of her son
Required difference = ( 31 ? 19 ) years = 12 years
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