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1. A couple has a son and a daughter. The age of the father is four times that of the son and the age of the daughter is one-third of that of her mother. The wife is 6 years younger to her husband and the sister is 3 years older then her brother. The mother's age is = ?

A. 42 years

B. 48 years

C. 54 years

D. 63 years

Solution:

M → Mother, F → Father, S → Son and D → Daughter
F = 4S, D =

\frac{1}{3}

M, M = F - 6 and S = D - 3

\begin{aligned} ∴ M = 3 D = 3 (S + 3) \\ = 3 S + 9 = \frac{3}{4} F + 9 = \frac{3}{4} (M + 6) + 9 \\ = \frac{3}{4} M + \frac{3}{4} \times 6 + 9 \\ \Rightarrow (M - \frac{3}{4} M) = (\frac{9}{2} + 9) \\ \Rightarrow \frac{1}{4} M = \frac{27}{2} \\ \Rightarrow M = (\frac{27}{2} \times 4) \\ = 54 years \\ ∴ The mother is 54 years old . \end{aligned}

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