Two shopkeepers announce the same price of ₹ 700 for a sewing machine. The first offers successive discounts of 30% and 6% while the second offers successive discounts of 20% and 16%. The shopkeeper that offers better discount, charges ......... less than the other shopkeeper. (M.A.T., 2009)

### Concept & Net Selling Price The final selling price after successive discounts can be found using the multiplier method. For a marked price $MP$ and discounts $d_1$ and $d_2$, the Selling Price ($SP$) is: $$SP = MP \times \left(1 - \frac{d_1}{100}\right) \times \left(1 - \frac{d_2}{100}\right)$$ ### Step-by-Step Solution * **Analyze First Shopkeeper:** * Marked Price ($MP$) = $700$ * Discounts = $30\%$ and $6\%$ * $SP_1 = 700 \times 0.70 \times 0.94$ * $SP_1 = 490 \times 0.94 = 460.60$ * **Analyze Second Shopkeeper:** * Marked Price ($MP$) = $700$ * Discounts = $20\%$ and $16\%$ * $SP_2 = 700 \times 0.80 \times 0.84$ * $SP_2 = 560 \times 0.84 = 470.40$ * **Find the Difference:** * The first shopkeeper charges ₹ $460.60$ and the second charges ₹ $470.40$. * The shopkeeper offering the better discount (the first one) charges less. * Difference = $470.40 - 460.60 = 9.80$ ### Exam Strategy & Shortcut Instead of finding absolute selling prices, you can calculate the equivalent discount percentage for both. Shopkeeper 1: $30 + 6 - (30 \times 6)/100 = 36 - 1.8 = 34.2\%$ Shopkeeper 2: $20 + 16 - (20 \times 16)/100 = 36 - 3.2 = 32.8\%$ Difference in discounts = $34.2\% - 32.8\% = 1.4\%$. Difference in price = $1.4\%$ of $700 = \frac{1.4}{100} \times 700 = 9.80$. ### Common Pitfall Students often assume that if the sum of the discounts is the same ($30+6 = 36$ and $20+16 = 36$), the final price is identical. Always account for the $-\frac{ab}{100}$ term. ### Final Answer Therefore, the correct answer is **₹ 9.80**.