A couple has a son and a daughter. The age of the father is four times the son and the age of the mother is three times the daughter. The mother is 6 years younger to the father and the daughter is 3 years older than the son. What is the age of the mother?

Question: A couple has a son and a daughter. The age of the father is four times the son and the age of the mother is three times the daughter. The mother is 6 years younger to the father and the daughter is 3 years older than the son. What is the age of the mother?

Solution:
Let, father, mother, son and daughter have age of F, M, S and D respectively.
ATQ,
F = 4S ………….(i)
M = 3D………….(ii)
M = F - 6………..(iii)
D = S + 3………..(iv)

From (ii) we get,
M = 3D
Or, M = 3(S + 3) [from (iv)]
Or, M = 3{(F/4) + 3} [from (i)]
Or, M = ¾(F + 12)
Or, M = ¾(M + 6 + 12) [from(iii)]
Or, M = ¾(M + 18)
Or, 4M = 3M + 54
Or, M = 54

∴ the age of the mother is 54 years.