A dealer marked the price of an item 40% above the cost price. He allowed two successive discounts of 20% and 25% to a particular customer. As a result he incurred a loss of ₹448. At what price did he sell the item to the said customer?

### Concept & Logic Successive discounts are calculated sequentially on the marked price. Let the Cost Price (CP) be $100x$ to simplify percentage calculations. ### Step-by-Step Solution 1. Let the Cost Price (CP) be $100x$. 2. The Marked Price (MP) is $40\%$ above CP: $$MP = 100x + 40x = 140x$$ 3. Two successive discounts of $20\%$ and $25\%$ are given on the MP. Equivalent multiplier for discounts = $(1 - 0.20) \times (1 - 0.25) = 0.80 \times 0.75 = 0.60$ Selling Price (SP) = $140x \times 0.60 = 84x$ 4. The dealer incurred a loss of ₹448. $$Loss = CP - SP$$ $$100x - 84x = 448$$ $$16x = 448$$ $$x = \frac{448}{16} = 28$$ 5. Find the Selling Price: $$SP = 84x = 84 \times 28 = 2352$$ ### Exam Strategy & Shortcut Net discount for $20\%$ and $25\% = -20 - 25 + \frac{(-20)(-25)}{100} = -45 + 5 = -40\%$. So, SP = $60\%$ of MP. MP = $140\%$ of CP. SP = $60\%$ of $140\%$ of CP = $84\%$ of CP. Loss = $16\%$ of CP. Given $16\%$ of CP = 448. We need to find $84\%$ of CP. $SP = \frac{448}{16} \times 84 = 28 \times 84 = 2352$. ### Common Pitfall A common mistake is adding successive discounts directly ($20\% + 25\% = 45\%$) instead of applying them sequentially, which leads to an incorrect selling price. ### Final Answer Therefore, the correct answer is **₹ 2,352**.