By selling an article at $\frac{2}{5}$ of the marked price, there is a loss of 25%. The ratio of the marked price and the cost price of the article is

### Concept & Equating Selling Price Express the Selling Price (SP) in terms of both the Marked Price (MP) and the Cost Price (CP) to find the ratio between MP and CP. ### Step-by-Step Solution - Let the Marked Price be MP and Cost Price be CP. - Given that the article is sold at $\frac{2}{5}$ of the marked price, so $\text{SP} = \frac{2}{5}\text{MP}$. - The transaction results in a loss of $25\%$. - Therefore, the selling price is $75\%$ of the cost price, so $\text{SP} = \frac{75}{100}\text{CP} = \frac{3}{4}\text{CP}$. - Since both expressions represent the Selling Price, equate them: - $\frac{2}{5}\text{MP} = \frac{3}{4}\text{CP}$ - Rearranging to find the ratio $\frac{\text{MP}}{\text{CP}}$: - $\frac{\text{MP}}{\text{CP}} = \frac{\frac{3}{4}}{\frac{2}{5}}$ - $\frac{\text{MP}}{\text{CP}} = \frac{3}{4} \times \frac{5}{2} = \frac{15}{8}$. - The ratio of Marked Price to Cost Price is $15:8$. ### Exam Strategy & Shortcut Translate the fractions immediately. Loss of $25\%$ means $\text{SP} = \frac{3}{4}\text{CP}$. We are given $\text{SP} = \frac{2}{5}\text{MP}$. So $\frac{3}{4}\text{CP} = \frac{2}{5}\text{MP}$. $\frac{\text{MP}}{\text{CP}} = \frac{3 \times 5}{4 \times 2} = \frac{15}{8}$. ### Common Pitfall Misaligning the ratio components by incorrectly cross-multiplying, leading to the reciprocal answer $8:15$. Always carefully isolate $\frac{\text{MP}}{\text{CP}}$. ### Final Answer Therefore, the correct answer is **15 : 8**.