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(D) Let the age of the mother be $x$ years.Age of the son $= \frac{x}{2}$ years.Since the brother (son) is $7$ years older than his sister (daughter),

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$60$

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(D) Let the age of the mother be $x$ years.Age of the son $= \frac{x}{2}$ years.Since the brother (son) is $7$ years older than his sister (daughter),the age of the daughter $= \frac{x}{2} - 7$ years.The age of the father is three times that of the daughter,so the age of the father $= 3 \left( \frac{x}{2} - 7 \right)$ years.Given that the wife (mother) is $9$ years younger than her husband (father),we have the equation: $x = 3 \left( \frac{x}{2} - 7 \right) - 9$.Alternatively,Father's age - Mother's age $= 9$,so $3 \left( \frac{x}{2} - 7 \right) - x = 9$.$\frac{3x}{2} - 21 - x = 9$.$\frac{x}{2} - 21 = 9$.$\frac{x}{2} = 30$.$x = 60$.Therefore,the age of the mother is $60$ years.

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 his mother. The wife is $9$ years younger than her husband and the brother is $7$ years older than his sister. What is the age of the mother? (in years)

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