MAT Exam 2024 Paper

Concept:The difference between compound interest and simple interest depends only on the principal, rate, and time. So, this difference can be used to find the principal and then the required compound interest.Explanation:Let the principal be $P$.Statement I:For 2 years at $5\%$ per annum,$\text{SI} = P \times \frac{5}{100} \times 2 = 0.10P$$\text{CI} = P\left[\left(1 + \frac{5}{100}\right)^2 - 1\right] = 0.1025P$So, $\text{CI} - \text{SI} = 0.1025P - 0.10P = 0.0025P$Given $\text{CI} - \text{SI} = 12.50$,$0.0025P = 12.50$$P = \frac{12.50}{0.0025} = 5000$Now, compound interest for 3 years at $5\%$:$\text{CI} = 5000\left[\left(1.05\right)^3 - 1\right]$$= 5000 \times 0.157625 = 788.125$So, Statement I alone is sufficient.Statement II:For 3 years at $5\%$ per annum,$\text{SI} = P \times \frac{5}{100} \times 3 = 0.15P$$\text{CI} = P\left[\left(1.05\right)^3 - 1\right] = 0.157625P$So, $\text{CI} - \text{SI} = 0.157625P - 0.15P = 0.007625P$Given $\text{CI} - \text{SI} = 38.125$,$0.007625P = 38.125$$P = \frac{38.125}{0.007625} = 5000$Then 3-year CI is again $5000 \times 0.157625 = 788.125$So, Statement II alone is also sufficient.Answer:Either statement alone is sufficient to answer the question.Hence, Option C is correct.The required compound interest after 3 years is ₹788.125.