A seller allows a discount of $5\%$ on a watch. If he allows a discount of $7\%$ he earns ₹ $15$ less in the profit. What is the marked price? (R.R.B., 2006)

### Concept & Logic When a seller increases the discount percentage on an item, their profit decreases by the exact amount of the additional discount. Therefore, the difference in the profit amounts directly corresponds to the difference in the discount percentages applied to the Marked Price (MP). $$ \text{Difference in Discount \%} \times \text{Marked Price} = \text{Difference in Profit} $$ ### Step-by-Step Solution * **Given:** * Initial discount = $5\%$ * New discount = $7\%$ * Decrease in profit = ₹ $15$ * **Calculation:** * Find the difference in the discount percentages: $7\% - 5\% = 2\%$ * This $2\%$ additional discount on the Marked Price is exactly equal to the ₹ $15$ reduction in profit. * So, $2\%$ of MP = ₹ $15$ * $\frac{2}{100} \times \text{MP} = 15$ * $\text{MP} = \frac{15 \times 100}{2} = 15 \times 50 = 750$ ### Exam Strategy & Shortcut To solve this mentally without writing down equations, just observe the percentage gap. The gap is $2\%$, which equals $15$. If $2\%$ is $15$, then $1\%$ is $7.5$. Therefore, $100\%$ (the full marked price) is $7.5 \times 100 = 750$. ### Common Pitfall A common mistake is assuming the ₹ $15$ difference applies to the Cost Price or the Selling Price. Always remember that discount percentages are universally calculated on the Marked Price (Labelled Price). ### Final Answer Therefore, the correct answer is **₹ 750**.