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 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?

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In such problems, define variables for unknown ages, form equations based on the given relationships, and solve systematically.
Updated On: Mar 10, 2025
  • 40 years
  • 50 years
  • 45 years
  • 60 years
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The Correct Option is D

Solution and Explanation

Step 1: Assume the daughter`s age.
Let the daughter`s age be x years.

Step 2: Express other ages.
The father`s age = 3x years.
The mother`s age = (3x - 9) years.
The son`s age = (x + 7) years.

Step 3: Set up an equation.
From the given condition that the son`s age is half of his mother`s age, we get:
\[ x + 7 = \frac{1}{2}(3x - 9) \]
Solving the equation:
\[ 2(x + 7) = 3x - 9 \]
\[ 2x + 14 = 3x - 9 \]
\[ 14 + 9 = 3x - 2x \]
\[ x = 23 \]

Step 4: Find the mother`s age.
The mother`s age = 3x - 9 = 3(23) - 9 = 69 - 9 = 60 years.

Step 5: Final Answer
The correct answer is (d) 60 years. Final Answer: The correct answer is (d) 60 years.
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