If on a marked price, the difference of selling prices with a discount of $30\%$ and two successive discounts of $20\%$ and $10\%$ is ₹ $72$, then the marked price (in ₹) is (S.S.C., 2010)

### Concept & Formula The difference in selling prices arises strictly from the difference in the effective discount percentages applied to the same Marked Price (MP). $$ \text{Difference in Discount \%} \times \text{MP} = \text{Difference in SP} $$ ### Step-by-Step Solution * **Given:** * Single discount = $30\%$ * Successive discounts = $20\%$ and $10\%$ * Difference in selling prices = ₹ $72$ * **Calculation:** * Calculate the single equivalent discount for $20\%$ and $10\%$: $20 + 10 - \frac{20 \times 10}{100} = 30 - 2 = 28\%$. * Find the difference between the two discount schemes: $30\% - 28\% = 2\%$. * This $2\%$ difference applied to the Marked Price results in the ₹ $72$ difference. $2\% \text{ of MP} = 72$ $\frac{2}{100} \times \text{MP} = 72$ $\text{MP} = \frac{72 \times 100}{2} = 36 \times 100 = 3600$. ### Exam Strategy & Shortcut When comparing a single discount of $(x+y)\%$ with successive discounts of $x\%$ and $y\%$, the percentage difference is always exactly $\frac{xy}{100}\%$. Here, difference $= \frac{20 \times 10}{100} = 2\%$. If $2\% = 72$, then $1\% = 36$, and $100\% = 3600$. This skips full equivalent discount calculation. ### Common Pitfall Mistakenly assuming that successive discounts of $20\%$ and $10\%$ equal a $30\%$ discount, which would lead to the conclusion that there is no price difference. ### Final Answer Therefore, the correct answer is **3600**.