MAT Exam 2023 Paper

Concept:Use two variables for the principal amounts and form simultaneous linear equations from the given interest conditions.Explanation:Let the amount invested at $20\%$ be $x$ and the amount at $25\%$ be $y$.The yearly interest is ₹130, so:$$0.20x + 0.25y = 130$$Multiply throughout by 100:$$20x + 25y = 13000$$If the amounts are interchanged, interest becomes ₹134:$$0.25x + 0.20y = 134$$Multiply throughout by 100:$$25x + 20y = 13400$$Now solve the two equations:Multiply the first by 4:$$80x + 100y = 52000$$Multiply the second by 5:$$125x + 100y = 67000$$Subtract the first result from the second:$$45x = 15000$$$$x = \frac{15000}{45} = 333\frac{1}{3}$$Answer:He invested ₹ $333\frac{1}{3}$ at $20\%$ simple interest.