MAT Exam 2025 Paper

Concept:Use a single variable for the original pass and fail counts, then apply the second condition to form a ratio equation.Explanation:Let the number of passed candidates be $5x$ and failed candidates be $x$.So, total candidates appeared $= 5x + x = 6x$.In the second scenario:New total candidates $= 6x + 21$.New passed candidates $= 5x - 11$.New failed candidates $= \text{Total} - \text{Passed}$$= (6x + 21) - (5x - 11) = x + 32$.Given the new ratio of passed to failed is $7 : 2$:$$\frac{5x - 11}{x + 32} = \frac{7}{2}$$Cross-multiply:$$2(5x - 11) = 7(x + 32)$$$$10x - 22 = 7x + 224$$$$3x = 246$$$$x = 82$$Original total number of candidates who appeared:$$6x = 6 \times 82 = 492$$Answer:492, i.e. Option D.