A manufacturer marked an article at ₹ 50 and sold it allowing 20% discount. If his profit was 25%, then the cost price of the article was

### Concept & MP to CP Conversion The Selling Price connects Marked Price and Cost Price. Calculate SP from MP and the discount, then use SP and the profit percentage to find CP. ### Step-by-Step Solution - Given Marked Price (MP) = Rs. 50. - Discount allowed = $20\%$ on MP. - Selling Price (SP) = $\text{MP} - (20\% \text{ of } \text{MP}) = 50 - (0.20 \times 50) = 50 - 10 = \text{Rs. } 40$. - The profit made is $25\%$ on the Cost Price (CP). - $\text{SP} = \text{CP} \times (1 + \frac{\text{Profit}\%}{100})$. - $40 = \text{CP} \times (1 + 0.25) = 1.25 \times \text{CP}$. - $\text{CP} = \frac{40}{1.25}$. - To remove the decimal, multiply numerator and denominator by 100: $\text{CP} = \frac{4000}{125}$. - $\text{CP} = 32$. ### Exam Strategy & Shortcut Use the direct ratio formula: $\frac{\text{CP}}{\text{MP}} = \frac{100 - \text{Discount}\%}{100 + \text{Profit}\%}$. $\frac{\text{CP}}{50} = \frac{100 - 20}{100 + 25} = \frac{80}{125}$. Simplify the fraction by dividing by 5: $\frac{16}{25}$. $\text{CP} = 50 \times (\frac{16}{25}) = 2 \times 16 = 32$. This is much faster. ### Common Pitfall A common error is to calculate the $25\%$ profit on the Selling Price (40) rather than the Cost Price, which would incorrectly yield a CP of 30. Profit is always based on Cost Price unless explicitly stated otherwise. ### Final Answer Therefore, the correct answer is **₹ 32**.