If the S.P. of ₹ 24 results in a 20% discount on list price, what S.P. would result in a 30% discount on list price?

### Concept & Direct Proportions The selling price (S.P.) is directly proportional to the remaining percentage of the list price after a discount. You can equate the ratios of S.P. to their corresponding percentages to find the unknown value directly. $$ \frac{\text{SP}_1}{100 - \text{Discount}_1} = \frac{\text{SP}_2}{100 - \text{Discount}_2} $$ ### Step-by-Step Solution * Let the list price of the article be $L$. * A $20\%$ discount means the Selling Price is $100\% - 20\% = 80\%$ of the list price. * We are given that this initial S.P. is ₹ 24. * $80\%$ of $L = 24 \implies 0.80 \times L = 24$. * $L = \frac{24}{0.80} = \frac{240}{8} = 30$. * The list price is ₹ 30. * We need to find the new S.P. for a $30\%$ discount. * A $30\%$ discount leaves $100\% - 30\% = 70\%$ of the list price. * New S.P. = $70\%$ of $30$. * New S.P. = $0.70 \times 30 = 21$. ### Exam Strategy & Shortcut Skip finding the list price entirely by using proportion. ₹ 24 represents $80\%$ of the total. We want to find what represents $70\%$ of the total. $\text{New S.P.} = 24 \times \left(\frac{70}{80}\right) = 24 \times \left(\frac{7}{8}\right) = 3 \times 7 = 21$. ### Common Pitfall Calculating the $30\%$ discount directly on the first selling price of ₹ 24 instead of recognizing that all discounts must be evaluated against the base list price. ### Final Answer Therefore, the correct answer is **₹ 21**.