MAT Exam 2024 Paper

Concept:Use variables for present ages and form equations from the given age relations.Explanation:Let Anil's present age be $x$ years and his father's present age be $y$ years.Given: Anil is one-fourth his father's age.So, $x = \frac{1}{4}y$.After 18 years, Anil's age will be $x + 18$ and his father's age will be $y + 18$.At that time, Anil will be half his father's age.So, $x + 18 = \frac{1}{2}(y + 18)$.Substitute $x = \frac{1}{4}y$ into this equation:$\frac{1}{4}y + 18 = \frac{1}{2}(y + 18)$$\Rightarrow \frac{y}{4} + 18 = \frac{y}{2} + 9$$\Rightarrow \frac{y}{2} - \frac{y}{4} = 18 - 9$$\Rightarrow \frac{y}{4} = 9$$\Rightarrow y = 36$ years.Answer:The present age of Anil's father is $36$ years, which is option B.