The average age of two boys and their father is greater then average age of those two boys and their mother by 3 yr. The average age of the four is 19 yr. If the average age of the two boys be 5 1/ 2, then find the age of the father and mother.

Let the ages of mother, father and boys be M, F, B₁ and B₂, respectively.
The total age of four member
= 19 x 4
= 76 yr.
Given (B₁ + B₁)/2 = 11/2
⇒ B₁ + B₂ = 11
M + F + B₁ + B₂ = 76 - 11
⇒ M + F = 65 .......(i)
According to the question,
(B₁ + B₂ + F) / 3 = (B₁ + B₂ + M) / 3 + 3
⇒ B₁ + B₂ + F) = B₁ + B₂ + M + 9
⇒ F = M + 9
⇒ F - M = 9 ............. (ii)
From Eqs (i) and (ii), we get
F = 37 yr and M = 28 yr