If the ratio of cost price and selling price of an article be 10 : 11, the percentage of profit is

### Concept & Profit Percentage The relationship between Cost Price (CP) and Selling Price (SP) can be used directly from their ratio to find the profit or loss. $$ \text{Profit \%} = \left(\frac{\text{SP} - \text{CP}}{\text{CP}}\right) \times 100 $$ ### Step-by-Step Solution * **Step 1:** Let the common ratio multiplier be $x$. * Cost Price (CP) = $10x$ * Selling Price (SP) = $11x$ * **Step 2:** Calculate the profit. * $\text{Profit} = \text{SP} - \text{CP} = 11x - 10x = 1x$ * **Step 3:** Calculate the percentage of profit. * $\text{Profit \%} = \left(\frac{1x}{10x}\right) \times 100$ * $\text{Profit \%} = \left(\frac{1}{10}\right) \times 100 = 10\%$ ### Exam Strategy & Shortcut When given a ratio, you can ignore the variable $x$ entirely and treat the ratio numbers as actual values. Assume CP = ₹ 10 and SP = ₹ 11. The profit is ₹ 1. The profit percentage is simply $\frac{1}{10} \times 100 = 10\%$. ### Common Pitfall A common mistake is placing the Selling Price (11) in the denominator instead of the Cost Price (10), which would lead to an incorrect calculation of $\frac{1}{11} \approx 9.09\%$. ### Final Answer Therefore, the correct answer is **10**.