The ratio between the sale price and the cost price of an article is $7 : 5$. What is the ratio between the profit and the cost price of that article?

### Concept & Ratio Relationships When a ratio between the Selling Price (SP) and Cost Price (CP) is given, we can represent them as multiples of a common variable. The profit is the difference between these two values. From there, any subsequent ratio involving Profit, SP, and CP can be determined. $$ \text{Profit} = \text{Selling Price} - \text{Cost Price} $$ ### Step-by-Step Solution * Given Ratio: $SP : CP = 7 : 5$ * Let Selling Price (SP) = $7x$ * Let Cost Price (CP) = $5x$ * Calculate Profit: $\text{Profit} = SP - CP = 7x - 5x = 2x$ * The question asks for the ratio between the profit and the cost price. * Required Ratio = $\text{Profit} : CP$ * Substitute the values: $2x : 5x$ * Cancel the common term $x$: The ratio is $2 : 5$. * Now, check the given options: (a) 2 : 7, (b) 5 : 2, (c) 7 : 2, (d) Data inadequate. * Since $2 : 5$ is not among the specific numeric options, the correct choice is "None of these". ### Exam Strategy & Shortcut Assume arbitrary convenient numbers that fit the ratio. Let SP = ₹ 7 and CP = ₹ 5. Profit = $7 - 5 = \text{₹ } 2$. Ratio of Profit to CP = $2 / 5 = 2 : 5$. Scanning the options immediately shows $2:5$ is missing, pointing directly to Option (e). ### Common Pitfall Misreading the requested ratio order. Students often accidentally choose the reciprocal $5:2$ (Option b) by finding the ratio of Cost Price to Profit, or they choose $2:7$ (Option a) by finding the ratio of Profit to Selling Price. ### Final Answer Therefore, the correct answer is **None of these**.