The simple interest on ₹ 1820 from March 9, 2012 to May 21, 2012 at $7\frac{1}{2}\%$ rate will be

### Concept & Formula When calculating simple interest between specific dates, count the exact number of days (excluding the start date, including the end date, or vice-versa) and divide by 365 to convert to years. $$SI = \frac{P \times R \times T \text{ (in years)}}{100}$$ ### Step-by-Step Solution * **Given:** * Principal ($P$) = ₹ 1820 * Rate ($R$) = $7\frac{1}{2}\%$ = $\frac{15}{2}\%$ * Dates: March 9, 2012 to May 21, 2012 * **Calculate Time in Days:** * March (31 days total): $31 - 9 = 22$ days left * April: $30$ days * May: $21$ days (up to May 21st) * Total Days = $22 + 30 + 21 = 73$ days * **Convert Time to Years:** * $T = \frac{73}{365} = \frac{1}{5}$ years (since $73 \times 5 = 365$) * **Calculate Interest:** * $SI = \frac{1820 \times (\frac{15}{2}) \times (\frac{1}{5})}{100}$ * $SI = \frac{1820 \times 15}{100 \times 10}$ * $SI = \frac{1820 \times 3}{200}$ * $SI = 9.1 \times 3 = 27.30$ ### Exam Strategy & Shortcut Recognize that 73 days is exactly $\frac{1}{5}$ of a standard 365-day year. This is a very common fraction used in competitive exams. Even though 2012 was a leap year, the period given is post-February, so the leap year does not affect the day count. Just multiply $182 \times 15 / 100$, giving $2730 / 100 = 27.30$. ### Common Pitfall Including both the start and end dates in the day calculation will result in 74 days, complicating the math and leading to an incorrect answer. Standard practice is to exclude the first day. ### Final Answer Therefore, the correct answer is **₹ 27.30**.