MAT Exam 2025 Paper

Concept:Simple interest is calculated as $SI = \frac{P \times R \times T}{100}$, while compound interest is calculated as $CI = P\left[\left(1+\frac{R}{100}\right)^T - 1\right]$.Explanation:Let the original sum be $P$.Using the given simple interest,$64800 = \frac{P \times 4.5 \times 3}{100}$$P = \frac{64800 \times 100}{13.5} = ₹4,80,000$The sum used for compound interest is $75\%$ of $P$:$\frac{3}{4} \times 4,80,000 = ₹3,60,000$The doubled rate is $4.5\% \times 2 = 9\%$ per annum.Now, calculate compound interest for 3 years:$CI = 3,60,000\left[\left(1+\frac{9}{100}\right)^3 - 1\right]$$= 3,60,000\left[(1.09)^3 - 1\right]$$= 3,60,000 \times 0.295029 = ₹1,06,210.44$Required difference between this CI and the given SI is:$= 1,06,210.44 - 64,800 = ₹41,410.44$So, the required difference is approximately ₹41,410.Answer:Option C — ₹41,410