Komal buys an article at a discount of 25%. At what percentage above the cost price should he sell it to make a profit of 25% over the original list price?

### Concept & Markup on Cost Price The phrasing "profit of 25% over the original list price" implies the new Selling Price should be 25% higher than the original list price. The target markup is calculated based on Komal's Cost Price. $$ \text{Markup Percentage} = \frac{\text{Target SP} - \text{Komal's CP}}{\text{Komal's CP}} \times 100 $$ ### Step-by-Step Solution * Let the original list price (Marked Price) of the article be 100. * Komal buys it at a 25% discount, so Komal's Cost Price (CP) = $100 - 25\% \text{ of } 100 = 75$. * He wants to make a profit of 25% *over the original list price*. This means his target Selling Price (SP) should be the original list price plus 25% of the original list price. * Target SP = $100 + 25\% \text{ of } 100 = 125$. * Komal's Profit = Target SP - Komal's CP = $125 - 75 = 50$. * The question asks: "At what percentage above the cost price should he sell it?". This is asking for the markup percentage relative to his CP. * Percentage above cost price = $\frac{50}{75} \times 100 = \frac{2}{3} \times 100$. * $\frac{2}{3} \times 100 = 66.66...\% \approx 66.67\%$. ### Exam Strategy & Shortcut Let List Price = 4 units. Komal buys at 25% off, so CP = 3 units. He wants SP to be 25% *over* List Price, so SP = 4 + 1 = 5 units. Markup on CP = SP - CP = 5 - 3 = 2 units. Markup % = $\frac{2}{3} \times 100 = 66.67\%$. Using small fractions (quarters) keeps calculations mental and instantaneous. ### Common Pitfall Misinterpreting "make a profit of 25% over the original list price" as meaning his absolute profit is equal to 25% of the list price (which would make SP = 100 and markup = 33.33%, an option not listed). In commercial math, "profit over X" often means the final sale price is $X \times (1 + \text{profit \%})$. ### Final Answer Therefore, the correct answer is **66.67**.