A trader buys a chair for ₹ 600 and sells it for ₹ 765 at a credit of 4 months. Reckoning money worth 6% p.a., his gain percent is

### Concept & True Discount (Present Value) When an item is sold on credit, the future selling price must be discounted to its "Present Worth" (PW) to determine the true profit made today. $$ \text{PW} = \frac{\text{Amount due}}{1 + \left(\frac{R \times T}{100}\right)} $$ ### Step-by-Step Solution * **Identify Given Values:** * Cost Price (CP) = ₹ 600 * Future Value of Selling Price = ₹ 765 * Time ($T$) = $4$ months = $\frac{4}{12}$ years = $\frac{1}{3}$ years. * Rate of Interest ($R$) = $6\%$ p.a. * **Calculate Present Worth of Selling Price:** * $\text{PW} = \frac{765}{1 + \left( \frac{6 \times 1/3}{100} \right)}$ * $\text{PW} = \frac{765}{1 + \left( \frac{2}{100} \right)} = \frac{765}{1.02}$ * $\text{PW} = 750$ rupees. * The effective immediate selling price is ₹ 750. * **Calculate True Gain Percentage:** * Gain = Effective SP - CP = $750 - 600 = 150$ rupees. * Gain % = $\left( \frac{150}{600} \right) \times 100 = \frac{1}{4} \times 100 = 25\%$. ### Exam Strategy & Shortcut For simple numbers, note that $6\%$ per year is equivalent to $2\%$ for 4 months (since 4 months is a third of a year). So, the future amount represents $102\%$ of the present value. $765 / 1.02 = 750$. Comparing 750 (SP) to 600 (CP) yields a 150 profit on 600, instantly giving $\frac{1}{4}$ or $25\%$. ### Common Pitfall A standard trap is ignoring the credit period entirely and calculating profit as $(765 - 600) / 600 = 27.5\%$. This fails to account for the time value of money, which the prompt explicitly states by saying "Reckoning money worth 6% p.a.". ### Final Answer Therefore, the correct answer is **25%**.