An article was sold for ₹ $y$ after giving a discount of $x$%. Then, its list price is

### Concept & Algebraic Formulation of Discount The selling price is the list price minus the percentage discount applied to that list price. You can isolate the list price variable using basic algebra to create a general formula. $$ \text{Selling Price} = \text{List Price} \times \left(1 - \frac{\text{Discount \%}}{100}\right) $$ ### Step-by-Step Solution * Let the unknown list price of the article be denoted as $L$. * A discount of $x\%$ is offered on the list price. * The reduction in price is $\frac{x}{100} \times L$. * The selling price is calculated as: $L - \left(\frac{x}{100} \times L\right)$. * Factoring out $L$, the selling price equals $L \times \left(1 - \frac{x}{100}\right)$. * Finding a common denominator for the term in parentheses: $L \times \left(\frac{100 - x}{100}\right)$. * We are given that the final selling price is ₹ $y$. * Therefore, $y = L \times \left(\frac{100 - x}{100}\right)$. * To isolate the list price $L$, multiply both sides by the reciprocal $\frac{100}{100 - x}$. * $L = y \times \left(\frac{100}{100 - x}\right) = \frac{100y}{100 - x}$. ### Exam Strategy & Shortcut Memorize the standard reverse-percentage formula: $\text{Base Value} = \frac{\text{Final Value} \times 100}{100 - \text{Percentage Drop}}$. Substituting the given variables ($y$ for Final Value and $x$ for Percentage Drop) immediately gives $\frac{100y}{100 - x}$ without needing algebraic derivation. ### Common Pitfall Choosing option (b) $\frac{100y}{1 - x}$ by confusing the decimal representation of a percentage with its integer form. The variable $x$ represents the integer percentage (e.g., 20), so it must be subtracted from 100, not 1. ### Final Answer Therefore, the correct answer is **$\frac{100y}{100 - x}$**.