The marked price of a watch was ₹ 820. A man bought the same for ₹ 570.72 after getting two successive discounts of which the first was 20%. The rate of second discount was (S.S.C., 2008)

### Concept & Calculating Unknown Discount The price reduces progressively with successive discounts. The formula linking Marked Price ($MP$), Selling Price ($SP$), and discounts ($d_1, d_2$) is: $$SP = MP \times \left(1 - \frac{d_1}{100}\right) \times \left(1 - \frac{d_2}{100}\right)$$ ### Step-by-Step Solution * **Given:** * Marked Price ($MP$) = ₹ $820$ * Final Selling Price ($SP$) = ₹ $570.72$ * First discount ($d_1$) = $20\%$ * **Find the price after the first discount:** * Intermediate Price = $820 \times \left(1 - \frac{20}{100}\right)$ * Intermediate Price = $820 \times 0.80 = 656$ * **Determine the amount of the second discount:** * The second discount reduces the price from ₹ $656$ to ₹ $570.72$. * Discount amount = $656 - 570.72 = 85.28$ * **Calculate the rate of the second discount ($d_2$):** * $d_2 = \left(\frac{Discount Amount}{Intermediate Price}\right) \times 100$ * $d_2 = \left(\frac{85.28}{656}\right) \times 100$ * $d_2 = \frac{8528}{656} = 13\%$ ### Exam Strategy & Shortcut Use the ratio method to keep calculations clean. $820 \rightarrow \text{drop } 20\% \rightarrow 656$ You need to go from $656$ to $570.72$. Look at the units digit: $6 \times \text{something} = \text{ends in } 2$. Options are $12\%$, $13\%$, $15\%$, $18\%$. $12\%$ discount means multiplier is $0.88$. $6 \times 8 = 48$ (ends in $8$). No. $13\%$ discount means multiplier is $0.87$. $6 \times 7 = 42$ (ends in $2$). Yes! You can confidently mark $13\%$ without doing full division. ### Common Pitfall Getting bogged down by the decimals ($570.72$) and making arithmetic errors during long division. Always look to eliminate options using unit digits where possible. ### Final Answer Therefore, the correct answer is **13%**.