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
Answer: Option C
Solution(By Examveda Team)
M → Mother, F → Father, S → Son and D → DaughterF = 4S, D = $$\frac{1}{3}$$M, M = F - 6 and S = D - 3
$$\eqalign{ & \therefore M = 3D = 3\left( {S + 3} \right) \cr & = 3S + 9 = \frac{3}{4}F + 9 = \frac{3}{4}\left( {M + 6} \right) + 9 \cr & = \frac{3}{4}M + \frac{3}{4} \times 6 + 9 \cr & \Rightarrow \left( {M - \frac{3}{4}M} \right) = \left( {\frac{9}{2} + 9} \right) \cr & \Rightarrow \frac{1}{4}M = \frac{{27}}{2} \cr & \Rightarrow M = \left( {\frac{{27}}{2} \times 4} \right) \cr & \,\,\,\,\,\,\,\,\,\,\,\,\,\,\, = 54\,{\text{years}} \cr & \therefore {\text{ The mother is 54 years old}}{\text{.}} \cr} $$
Related Questions on Problems on Ages
A. 2 times
B. $$2\frac{1}{2}\,{\text{times}}$$
C. $$2\frac{3}{4}\,{\text{times}}$$
D. 3 times
A. 4 years
B. 8 years
C. 10 years
D. None of these
A. 14 years
B. 19 years
C. 33 years
D. 38 years
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