A trader sells an article and loses $12 \frac{1}{2}\%$. The ratio of cost price to the selling price is

### Concept & Fractional Equivalents Understanding the fractional equivalent of standard percentages makes ratio calculations instantaneous. Loss is calculated on the Cost Price (CP). $$ \text{SP} = \text{CP} - \text{Loss} $$ ### Step-by-Step Solution * **Step 1:** Convert the loss percentage to a fraction. * $12 \frac{1}{2}\% = \frac{25}{2}\% = \frac{25}{200} = \frac{1}{8}$ * **Step 2:** Interpret the fraction. * A loss of $\frac{1}{8}$ means for every $8$ units of Cost Price, there is a loss of $1$ unit. * Let $\text{CP} = 8$ units. * $\text{Loss} = 1$ unit. * **Step 3:** Calculate the Selling Price (SP). * $\text{SP} = \text{CP} - \text{Loss} = 8 - 1 = 7$ units. * **Step 4:** Determine the required ratio of Cost Price to Selling Price. * $\text{Ratio} = \text{CP} : \text{SP} = 8 : 7$ ### Exam Strategy & Shortcut Memorize that $12.5\%$ is exactly $\frac{1}{8}$. This immediately tells you that the SP is $1 - \frac{1}{8} = \frac{7}{8}$ of the CP. Therefore, the ratio of CP to SP is simply $8 : 7$. ### Common Pitfall Pay close attention to the order requested in the question. Students often calculate the ratio correctly but accidentally choose $7 : 8$ (which is SP to CP) instead of the requested CP to SP ($8 : 7$). ### Final Answer Therefore, the correct answer is **8 : 7**.