A showroom owner sells a leather jacket for ₹ X and claims to make a profit of 10%. He plans to have a stall in the trade fair and marks the same jacket at ₹ 2X. At the stall, he allows a discount of 20%. What will be the percentage profit that he will make at the trade fair? (M.B.A., 2006)

### Concept & Variable Substitution When dealing with variables like $X$ representing price points, substitute a concrete baseline number (like $100$) for the Cost Price to easily map out the entire sequence of markups and discounts without algebraic clutter. ### Step-by-Step Solution * **Establish Initial Scenario:** * Let the Cost Price (CP) of the jacket be $100$. * The owner claims a profit of $10\%$ when selling for ₹ $X$. * Therefore, initial Selling Price ($X$) = $100 + 10 = 110$. * So, $X = 110$. * **Establish Trade Fair Scenario:** * The new Marked Price is ₹ $2X$. * New Marked Price = $2 \times 110 = 220$. * He allows a discount of $20\%$ on this new Marked Price. * Discount Amount = $20\%$ of $220 = 44$. * **Calculate Final Profit:** * Final Selling Price = $220 - 44 = 176$. * Final Profit = Final SP - CP = $176 - 100 = 76$. * Since the CP is $100$, the profit percentage is $76\%$. ### Exam Strategy & Shortcut Relate everything as a multiplier of CP. $X = 1.1 \times CP$. Trade fair marked price = $2X = 2.2 \times CP$. Discount is $20\%$, meaning the multiplier is $0.8$. Final SP = $0.8 \times (2.2 \times CP) = 1.76 \times CP$. A multiplier of $1.76$ directly equates to a $76\%$ profit. ### Common Pitfall A common pitfall is assuming $X$ is the Cost Price instead of the initial Selling Price. The problem explicitly states he "sells... for ₹ X and claims to make a profit", making $X$ the SP. ### Final Answer Therefore, the correct answer is **76%**.