MAT Exam 2024 Paper

Concept:Form an equation using the relationship between the two numbers and their given sum.Explanation:Let the larger number be $x$.According to the question, the smaller number is one-fourth of the larger number.So, the smaller number $= \frac{x}{4}$.The sum of the two numbers is $45$.Thus, $x + \frac{x}{4} = 45$.Combine the terms: $\frac{4x + x}{4} = 45$.So, $\frac{5x}{4} = 45$.Multiply both sides by $4$: $5x = 180$.Therefore, $x = \frac{180}{5} = 36$.Now, the smaller number $= \frac{x}{4} = \frac{36}{4} = 9$.Answer:The smaller number is $9$, which corresponds to option D.