Manoj sold an article for ₹ $15000$. Had he offered a discount of $10\%$ on the selling price he would have earned a profit of $8\%$. What is the cost price? (Bank P.O., 2009)

### Concept & Formula The problem requires finding the Cost Price (CP) when a hypothetical Selling Price (SP) and Profit percentage are given. First, apply the discount to the original SP to find the new hypothetical SP, then use the profit formula to reverse-engineer the CP. $$ \text{Cost Price (CP)} = \frac{\text{Selling Price} \times 100}{100 + \text{Profit \%}} $$ ### Step-by-Step Solution * **Given:** * Original Selling Price = ₹ $15000$ * Hypothetical Discount = $10\%$ (applied to the original Selling Price) * Resulting Profit = $8\%$ * **Calculation:** * Find the hypothetical Selling Price after the $10\%$ discount: $\text{Discount} = 10\% \text{ of } 15000 = 1500$. $\text{New SP} = 15000 - 1500 = ₹ 13500$. * At this New SP of ₹ $13500$, the profit is $8\%$. This means the New SP is $108\%$ of the Cost Price. * $1.08 \times \text{CP} = 13500$ * $\text{CP} = \frac{13500}{1.08} = \frac{13500 \times 100}{108}$ * Simplify the fraction: $108$ goes into $13500$ exactly $125$ times ($108 \times 125 = 13500$). * $\text{CP} = 125 \times 100 = 12500$. ### Exam Strategy & Shortcut Instead of calculating the absolute discount amount, calculate the new SP directly using multipliers: $15000 \times 0.9 = 13500$. Then immediately map $108\% \rightarrow 13500$. Since $108 \times 10 = 1080$, $108 \times 100 = 10800$. $13500 - 10800 = 2700$, which is $108 \times 25$. So $108 \times 125 = 13500$. Therefore, $100\% = 12500$. ### Common Pitfall Students often mistakenly apply the discount to a presumed Marked Price rather than reading carefully that the problem explicitly says "discount of $10\%$ on the selling price". Always apply percentages to the base stated in the text. ### Final Answer Therefore, the correct answer is **₹ 12500**.