## Answer & Solution

Answer:** Option C**

Solution:

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

F = 4S, D = $$\frac{1}{3}$$M, M = F - 6 and S = D - 3

$$\eqalign{
& \therefore M = 3D = 3\left( {S + 3} \right) \cr
& = 3S + 9 = \frac{3}{4}F + 9 = \frac{3}{4}\left( {M + 6} \right) + 9 \cr
& = \frac{3}{4}M + \frac{3}{4} \times 6 + 9 \cr
& \Rightarrow \left( {M - \frac{3}{4}M} \right) = \left( {\frac{9}{2} + 9} \right) \cr
& \Rightarrow \frac{1}{4}M = \frac{{27}}{2} \cr
& \Rightarrow M = \left( {\frac{{27}}{2} \times 4} \right) \cr
& \,\,\,\,\,\,\,\,\,\,\,\,\,\,\, = 54\,{\text{years}} \cr
& \therefore {\text{ The mother is 54 years old}}{\text{.}} \cr} $$