The compound interest accrued on an amount of ₹ 25500 at the end of 3 years is ₹ 8440.50. What would be the simple interest accrued on the same amount at the same rate in the same period?

### Concept & Formula Total Amount under compound interest: $$A = P + CI = P \left(1 + \frac{R}{100}\right)^T$$ Simple Interest formula: $$SI = \frac{P \times R \times T}{100}$$ ### Step-by-Step Solution 1. **Find the Rate of Interest ($R$):** * $P = \text{₹ } 25500$, $CI = \text{₹ } 8440.50$, $T = 3\text{ years}$ $$A = 25500 + 8440.50 = \text{₹ } 33940.50$$ $$\frac{A}{P} = \left(1 + \frac{R}{100}\right)^3$$ $$\left(1 + \frac{R}{100}\right)^3 = \frac{33940.50}{25500} = \frac{339405}{255000} = \frac{1331}{1000} = \left(\frac{11}{10}\right)^3$$ $$1 + \frac{R}{100} = \frac{11}{10} \implies \frac{R}{100} = \frac{1}{10} \implies R = 10\%$$ 2. **Calculate the Simple Interest ($SI$):** $$SI = \frac{25500 \times 10 \times 3}{100} = 255 \times 30 = \text{₹ } 7650$$ ### Exam Strategy & Shortcut Recognize the ratio $\frac{A}{P} = \frac{33940.5}{25500} = 1.331 = (1.1)^3$, which immediately indicates $R = 10\%$. Then: $$SI = 30\% \text{ of } 25500 = 0.30 \times 25500 = \text{₹ } 7650$$ ### Common Pitfall Lengthy division without simplifying fractions to detect standard cube powers like $1331/1000$. ### Final Answer Therefore, the correct answer is **₹ 7650**.