If an article is sold at 200 percent profit, then the ratio of its cost price to its selling price will be

### Concept & Cost to Selling Price Ratio Profit is calculated based on the Cost Price (CP). When the profit is given as a percentage, you can assume the CP is $100\%$ (or $1$ part) to easily deduce the Selling Price (SP). $$ \text{SP} = \text{CP} + \text{Profit} $$ ### Step-by-Step Solution * **Step 1:** Assume a value for the Cost Price (CP). Let it be $x$. * Let $\text{CP} = x$ * **Step 2:** Express the profit in terms of $x$. * $\text{Profit} = 200\% \text{ of CP} = \left(\frac{200}{100}\right) \times x = 2x$ * **Step 3:** Calculate the Selling Price (SP). * $\text{SP} = \text{CP} + \text{Profit}$ * $\text{SP} = x + 2x = 3x$ * **Step 4:** Find the ratio of Cost Price to Selling Price. * $\text{Ratio} = \frac{\text{CP}}{\text{SP}} = \frac{x}{3x}$ * $\text{Ratio} = 1 : 3$ ### Exam Strategy & Shortcut Always let CP = $100$ for simple percentage problems. If Profit = $200$, then SP = CP + Profit = $100 + 200 = 300$. The ratio of CP : SP is simply $100 : 300$, which reduces instantly to $1 : 3$. ### Common Pitfall A common mistake is assuming that "200 percent profit" means the Selling Price is twice the Cost Price. This confuses "profit" with "selling price". If SP is twice CP, the profit is only $100\%$. A $200\%$ profit means the SP is three times the CP. ### Final Answer Therefore, the correct answer is **1 : 3**.