Ram borrows ₹ 520 from Gaurav at a simple interest of 13% per annum. What amount of money should Ram pay to Gaurav after 6 months to be absolved of the debt?

### Concept & Formula The amount to clear a debt is the Principal plus the Simple Interest. When the time is given in months, it must be converted to years by dividing by 12, since the interest rate is per annum. $$Amount = P + \frac{P \times R \times T}{100}$$ ### Step-by-Step Solution * **Given:** * Principal ($P$) = ₹ 520 * Rate ($R$) = 13% p.a. * Time ($T$) = 6 months = $\frac{6}{12}$ years = $\frac{1}{2}$ years * **Calculate Simple Interest:** * $SI = \frac{520 \times 13 \times (\frac{1}{2})}{100}$ * $SI = \frac{520 \times 13}{200}$ * $SI = \frac{6760}{200} = 33.80$ * **Calculate Total Amount:** * $Amount = 520 + 33.80 = 553.80$ ### Exam Strategy & Shortcut $13\%$ for a full year means $6.5\%$ for a half-year (6 months). Interest = $6.5\%$ of $520 = 5.2 \times 6.5 = 33.8$. Total Amount = $520 + 33.8 = 553.80$. This cuts down formula setup time. ### Common Pitfall A frequent error is forgetting to add the principal to the calculated interest. Always verify if the question asks for the "interest" or the "amount to be absolved of the debt". ### Final Answer Therefore, the correct answer is **₹ 553.80**.