On a sum of money, the simple interest for 2 years is ₹ 660, while the compound interest is ₹ 696.30, the rate of interest being the same in both the cases. The rate of interest is

### Concept & Difference between CI and SI For the first year, Simple Interest (SI) and Compound Interest (CI) are identical. The difference in the second year is purely the interest earned on the first year's interest. ### Step-by-Step Solution 1. **Find SI per year:** Total SI for 2 years = ₹ 660 SI for 1 year = $\frac{660}{2}$ = ₹ 330 2. **Find the difference between CI and SI for 2 years:** Difference = CI - SI = $696.30 - 660 = 36.30$ 3. **Determine the rate of interest ($R$):** This ₹ 36.30 is exactly the interest generated in the second year on the first year's interest of ₹ 330. $R = \left(\frac{36.30}{330}\right) \times 100$ $R = \left(\frac{363}{3300}\right) \times 100 = 11\%$ 4. **Compare with options:** The calculated rate is 11%, which is not present in options (a), (b), or (c). ### Exam Strategy & Shortcut Always remember: for 2 years, $\text{Difference} = \frac{SI \times R}{2 \times 100}$. $36.30 = \frac{660 \times R}{200} \implies R = \frac{36.30 \times 200}{660} = \frac{7260}{660} = 11\%$. Scanning the options immediately points to "None of these". ### Common Pitfall Students often try to set up complex quadratic equations involving the principal $P$, which wastes significant time. Use the direct relationship between SI and CI difference. ### Final Answer Therefore, the correct answer is **None of these**.