Question

In a family, a couple has a son and a daughter. The age of the father is three times that of his daughter and the age of the son is half of that of his mother. The wife is $9$ years younger to her husband and the brother is seven years older than his sister. What is the age of the mother?

• A. $40$ years
• B. $45$ years
• C. $50$ years
• D. $60$ years

Answer 1

Answer: (D)

$60$ years

Let the daughter's age be $x$ years.
Then, father's age $=\left(3x\right)$ years.
Mother's age $=(3x-9)$ years; Son's age $=(x+7)$ years.
So, $x+7=(3x-9)/2\iff 2x+14=3x-9\iff x=23$.
Therefore Mother's age $=(3x-9)=(69-9)$ years $=60$ years.