MAT Exam 2025 Paper

Concept:Represent Raja's and Laila's present ages using a common ratio multiplier.Explanation:Let Raja's present age be $2x$ and Laila's present age be $5x$.This matches the condition that Raja's age is $\frac{2}{5}$ of Laila's age.After 2 years, Raja's age will be $2x+2$ and Laila's age will be $5x+2$.Given: Laila's age after 2 years is 2 times Raja's age after 2 years.So, we write:$$5x+2 = 2(2x+2)$$Simplify the equation:$$5x+2 = 4x+4$$$$5x - 4x = 4 - 2$$$$x = 2$$Now, Raja's present age is:$$2x = 2(2) = 4$$Thus, Laila's present age is $5x = 10$.Verify the other condition: two years back, Laila's age was $10-2=8$ and Raja's age was $4-2=2$.Indeed, $8 = 4 \times 2$, so the condition is satisfied.Answer:The present age of Raja is 4 years.Correct option: C. 4.