Profit earned by selling an article for ₹ 1060 is 20% more than the loss incurred by selling the article for ₹ 950. At what price should the article be sold to earn 20% profit?

### Concept & Profit Relative to Loss This requires translating a percentage relationship into an algebraic equation. If the profit is $20\%$ more than the loss, the profit equals $120\%$ of the loss (or $1.2 \times \text{Loss}$). $$ \text{Profit} = \text{Loss} \times \left(1 + \frac{20}{100}\right) $$ ### Step-by-Step Solution * Let the Cost Price (C.P.) of the article be $x$. * Loss incurred when sold for ₹ $950 = x - 950$. * Profit earned when sold for ₹ $1060 = 1060 - x$. * The profit is $20\%$ more than the loss: * $1060 - x = (1.2) \times (x - 950)$ * Expand the right side: * $1060 - x = 1.2x - 1140$ * Add $x$ to both sides and $1140$ to both sides: * $1.2x + x = 1060 + 1140$ * $2.2x = 2200$ * $x = \frac{2200}{2.2} = 1000$. The Cost Price is ₹ 1000. * We need the selling price to earn a $20\%$ profit: * $\text{New S.P.} = 1000 \times 1.2 = 1200$. ### Exam Strategy & Shortcut Look at the total gap between the two selling prices: $1060 - 950 = 110$. This gap covers the loss amount plus the profit amount. The ratio of Loss to Profit is $100 : 120$, which simplifies to $5 : 6$. Divide the total gap ($110$) into $11$ parts ($5+6$). One part is $10$. Loss is $5$ parts = $50$. $\text{C.P.} = 950 + 50 = 1000$. $20\%$ profit on $1000$ is $200$. Final S.P. is $1200$. Since $1200$ is not in the options, select "None of these". ### Common Pitfall A frequent error is calculating "20% more" incorrectly by adding $20$ directly or misplacing the multiplier (e.g., making the Loss $1.2$ times the Profit). Ensure the modifier applies to the correct variable. ### Final Answer Therefore, the correct answer is **None of these**.