A shopkeeper gives two successive discounts on an article marked ₹ 450. The first discount given is 10%. If the customer pays ₹ 344.25 for the article, the second discount given is (S.S.C., 2006)

### Concept & Successive Discounts When two successive discounts are applied to a Marked Price ($MP$), the final Selling Price ($SP$) is calculated step-by-step. The first discount is applied to the $MP$, and the second discount is applied to the resulting discounted price. $$SP = MP \times \left(1 - \frac{d_1}{100}\right) \times \left(1 - \frac{d_2}{100}\right)$$ ### Step-by-Step Solution * **Given:** * Marked Price ($MP$) = ₹ $450$ * First Discount ($d_1$) = $10\%$ * Final Selling Price ($SP$) = ₹ $344.25$ * **Calculate price after first discount:** * Discount amount = $10\%$ of $450 = 45$ * Price after 1st discount = $450 - 45 = 405$ * **Calculate the second discount:** * The customer pays ₹ $344.25$ on the new price of ₹ $405$. * Discount amount = $405 - 344.25 = 60.75$ * **Calculate the percentage of the second discount ($d_2$):** * $d_2 = \left(\frac{60.75}{405}\right) \times 100$ * $d_2 = \frac{6075}{405} = 15\%$ ### Exam Strategy & Shortcut Work with multipliers for speed. $450 \times 0.9 \times (1 - x) = 344.25$ $405 \times (1 - x) = 344.25$ $(1 - x) = \frac{344.25}{405} = 0.85$ This immediately tells you the multiplier is $0.85$, meaning the discount is $15\%$. ### Common Pitfall A common error is calculating the second discount percentage on the original marked price (₹ $450$) instead of the intermediate discounted price (₹ $405$). Successive discounts must be applied sequentially. ### Final Answer Therefore, the correct answer is **15%**.