MAT Exam 2022 Paper

Concept:Apply the percentage change to the original ratio parts and simplify the new ratio.Explanation:Let the original number of boys and girls be $5x$ and $4x$ respectively.After a $30\%$ decrease, boys become $5x \times \frac{70}{100} = \frac{7x}{2}$.After a $5\%$ increase, girls become $4x \times \frac{105}{100} = \frac{21x}{5}$.New ratio $= \frac{7x}{2} : \frac{21x}{5}$.Multiply both terms by $10$ to remove fractions: $35x : 42x$.Simplify by dividing both terms by $7x$: $5 : 6$.Answer:New ratio is $5:6$, which is Option A.