The cost price of an article is 64% of the marked price. Calculate the gain percent after allowing a discount of 12%.

### Concept & Percentage Base When values are given in relative percentages (CP is a % of MP), assume a base value of 100 for the Marked Price to simplify calculations. ### Step-by-Step Solution - Let the Marked Price (MP) of the article be Rs. 100. - The Cost Price (CP) is given as $64\%$ of the MP. - Therefore, CP = $64\%$ of 100 = Rs. 64. - A discount of $12\%$ is allowed on the Marked Price. - Discount Amount = $12\%$ of 100 = Rs. 12. - Selling Price (SP) = MP - Discount = $100 - 12 = \text{Rs. } 88$. - Gain = SP - CP = $88 - 64 = \text{Rs. } 24$. - Gain Percentage = $(\frac{\text{Gain}}{\text{CP}}) \times 100 = (\frac{24}{64}) \times 100$. - Simplifying the fraction: $\frac{24}{64} = \frac{3}{8}$. - Gain Percentage = $\frac{3}{8} \times 100 = 37.5\%$. ### Exam Strategy & Shortcut Set MP = 100. CP = 64. SP after $12\%$ discount = 88. Profit = 24 on a base of 64. $\frac{24}{64} = \frac{3}{8}$. Knowing standard fraction-to-percentage conversions, $\frac{3}{8}$ directly translates to $37.5\%$. ### Common Pitfall A frequent error is calculating the final gain percentage based on the Marked Price (100) instead of the actual Cost Price (64), which would yield an incorrect answer of $24\%$. ### Final Answer Therefore, the correct answer is **37.5%**.