A shopkeeper sells 25 articles at ₹ 45 per article after giving 10% discount and earns 50% profit. If the discount is not given, the profit gained is

### Concept & Discount Logic The number of articles sold is redundant information when dealing purely with uniform percentages. Focus on a single article. $$ \text{MP} = \frac{\text{SP}}{1 - D\%} $$ ### Step-by-Step Solution * Let's consider a single article. The given Selling Price (SP) after a 10% discount is ₹ 45. * Marked Price (MP) = $\frac{45}{0.90} = 50$. * The profit earned at this SP (₹ 45) is 50%. * Cost Price (CP) = $\frac{45}{1.50} = 30$. * If no discount is given, the article is sold at its Marked Price, so the new SP = ₹ 50. * New Profit = $\text{MP} - \text{CP} = 50 - 30 = 20$. * New Profit % = $\frac{20}{30} \times 100 = 66 \frac{2}{3}\%$. ### Exam Strategy & Shortcut Using the ratio formula $$ \frac{\text{MP}}{\text{CP}} = \frac{100 + P\%}{100 - D\%} $$ $$ \frac{\text{MP}}{\text{CP}} = \frac{150}{90} = \frac{5}{3} $$ If sold at MP (no discount), profit is $\frac{5-3}{3} = \frac{2}{3} = 66 \frac{2}{3}\%$. The ₹ 45 and 25 articles are completely irrelevant. ### Common Pitfall Using the 25 articles to find total SP (₹ 1125) and proceeding with large numbers. This slows down the calculation significantly without changing the final percentage. ### Final Answer Therefore, the correct answer is **$66 \frac{2}{3}\%$**.