Subject: General Aptitude · Chapter: Problems on Ages · Exam: · Marks: · Difficulty:
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 than her brother. The mother's age is (P.C.S., 2008)
(a)42 years
(b)48 years
(c)54 years
(d)63 years
Answer
Answer (as printed): C
Explanation
M-Mother, F-Father, S-Son and D-Daughter. $$\mathrm{F}=4S,\ \mathrm{D}=\frac{1}{3}\mathrm{M},\ \mathrm{M}=\mathrm{F}-6,\ \mathrm{S}=\mathrm{D}-3$$ $$\mathrm{M}=3\mathrm{D}=3(S+3)=3S+9=\frac{3}{4}F+9=\frac{3}{4}(\mathrm{M}+6)+9$$ $$\Rightarrow \left(\mathrm{M}-\frac{3}{4}\mathrm{M}\right)=\left(\frac{9}{2}+9\right) \Rightarrow \frac{1}{4}\mathrm{M}=\frac{27}{2} \Rightarrow \mathrm{M}=\left(\frac{27}{2}\times 4\right)=54\text{ years.}$$ The mother is 54 years old.
Explanation as extracted from the printed page; notation may be imperfect.