MAT Exam 2022 Paper

Concept:Form linear equations from the family relationships and solve them step by step.Explanation:Let the daughter’s age be $x$ years.Then the father’s age is $3x$ years, because the father is three times as old as his daughter.The mother is 9 years younger than the father, so mother’s age is $(3x - 9)$ years.The brother is 7 years older than his sister, so the son’s age is $(x + 7)$ years.The son’s age is half of his mother’s age, so write the equation:$$x + 7 = \frac{3x - 9}{2}$$Multiply both sides by 2:$$2x + 14 = 3x - 9$$Rearrange the terms:$$14 + 9 = 3x - 2x$$$$x = 23$$Now, mother’s age is:$$3x - 9 = 3(23) - 9 = 69 - 9 = 60 \text{ years}$$Answer:The mother’s age is 60 years, i.e. Option D.