The difference between compound interest and simple interest on a sum for 2 years at 8 per cent is ₹ 768. The sum is

### Concept & Formula The difference between Compound Interest (CI) and Simple Interest (SI) for exactly 2 years on a principal $P$ at a rate of $R\%$ per annum is given by the formula: $$D_2 = P \left(\frac{R}{100}\right)^2$$ ### Step-by-Step Solution 1. **Extract Given Values:** Difference for 2 years ($D_2$) = ₹ 768 Rate of interest ($R$) = $8\%$ Time ($T$) = 2 years 2. **Apply the 2-Year Difference Formula:** $$768 = P \left(\frac{8}{100}\right)^2$$ $$768 = P \left(\frac{64}{10000}\right)$$ 3. **Solve for Principal ($P$):** $$P = \frac{768 \times 10000}{64}$$ $$P = 12 \times 10000$$ $$P = \text{₹ } 120000$$ ### Exam Strategy & Shortcut The difference essentially arises from the interest calculated on the first year's interest. First year's interest rate = $8\%$. Interest on that $8\%$ in the second year = $8\%$ of $8\% = 0.64\%$. So, $0.64\%$ of the Principal = 768. $$P = \frac{768}{0.64} \times 100 = 1200 \times 100 = \text{₹ } 120000$$ ### Common Pitfall Using the 3-year difference formula or mistakenly computing $D = P \times \frac{R^2}{100}$ instead of dividing by $10000$. ### Final Answer Therefore, the correct answer is **₹ 120000**.