If $5\%$ more is gained by selling an article for ₹ 350 than by selling it for ₹ 340, the cost of the article is

### Concept & Proportional Difference The difference between two selling prices directly corresponds to the difference in their respective profit percentages. Both percentages share the exact same base, which is the Cost Price (CP). $$ \Delta \text{SP} = (\Delta \text{Profit \%}) \times \text{CP} $$ ### Step-by-Step Solution * Given: * Selling Price 1 ($\text{SP}_1$) = ₹ 340 * Selling Price 2 ($\text{SP}_2$) = ₹ 350 * Additional gain percentage = $5\%$ * Calculate the absolute difference in Selling Price: * Difference in SP = $\text{SP}_2 - \text{SP}_1$ * Difference in SP = $350 - 340 = \text{₹ 10}$ * This difference in money corresponds strictly to the additional profit percentage gained on the Cost Price (CP). * $5\%$ of CP = ₹ 10 * $\frac{5}{100} \times \text{CP} = 10$ * Solve for CP: * $\text{CP} = \frac{10 \times 100}{5}$ * $\text{CP} = 2 \times 100 = 200$ ### Exam Strategy & Shortcut Equate the percentages directly to the currency values in your head. The gap in price is $350 - 340 = 10$. The gap in profit is $5\%$. Therefore, $5\%$ represents 10. To find $100\%$ (the full CP), multiply both sides by 20. $10 \times 20 = 200$. ### Common Pitfall Assuming that the $5\%$ gain applies to the selling prices directly rather than the hidden Cost Price. Always remember that profit percentages are tied to the CP. ### Final Answer Therefore, the correct answer is **₹ 200**.