Even after reducing the marked price of a transistor by ₹ 32, a shopkeeper makes a profit of 15%. If the cost price be ₹ 320, what percentage of profit would he have made if he had sold the transistor at the marked price?

### Concept & Profit on Marked Price To find the profit percentage when sold at the Marked Price, we must first establish the current Selling Price using the Cost Price and the actual Profit Percentage, then add the discount back to find the Marked Price. $$ \text{SP} = \text{CP} \times \left(1 + \frac{\text{Profit \%}}{100}\right) $$ $$ \text{MP} = \text{SP} + \text{Discount} $$ ### Step-by-Step Solution * Given the Cost Price (CP) of the transistor is ₹ 320. * The shopkeeper makes a profit of 15% on this CP. * Profit amount = $15\% \text{ of } 320 = \frac{15}{100} \times 320 = 48$. * The actual Selling Price (SP) = $\text{CP} + \text{Profit} = 320 + 48 = 368$. * This SP is achieved after reducing the marked price by ₹ 32 (which is the discount). * Marked Price (MP) = $\text{SP} + \text{Discount} = 368 + 32 = 400$. * If he had sold the transistor at the marked price, his new Selling Price would be ₹ 400. * New Profit = $\text{MP} - \text{CP} = 400 - 320 = 80$. * New Profit Percentage = $\frac{\text{New Profit}}{\text{CP}} \times 100 = \frac{80}{320} \times 100$. * $\frac{1}{4} \times 100 = 25\%$. ### Exam Strategy & Shortcut Instead of calculating the full SP and MP, think in terms of additional profit. The current profit is 15%. If the discount of ₹ 32 is NOT given, this ₹ 32 becomes additional profit. What percentage of the CP (₹ 320) is this additional profit? $\frac{32}{320} \times 100 = 10\%$. Total profit percentage = Current Profit % + Additional Profit % = $15\% + 10\% = 25\%$. This completely bypasses intermediate arithmetic! ### Common Pitfall Calculating the new profit percentage on the Marked Price instead of the Cost Price. Profit percentage is always evaluated on the CP unless explicitly stated otherwise. ### Final Answer Therefore, the correct answer is **25%**.