1. **Problem Statement:** A trader marks goods 80% above the cost price, gives successive discounts of 15% and 10%, and 5% of the goods are damaged and sold at a 40% loss. We need to find the overall profit or loss percentage. 2. **Step 1: Define variables and mark price** Let the cost price (CP) be $100$ units. The marked price (MP) is 80% above CP, so: $$MP = 100 + 0.8 \times 100 = 180$$ 3. **Step 2: Calculate the selling price after successive discounts** First discount of 15% on MP: $$SP_1 = MP \times (1 - 0.15) = 180 \times 0.85 = 153$$ Second discount of 10% on $SP_1$: $$SP_2 = SP_1 \times (1 - 0.10) = 153 \times 0.90 = 137.7$$ 4. **Step 3: Account for damaged goods** 5% of goods are damaged and sold at 40% loss. - Cost price of damaged goods = $5$ units (5% of 100) - Selling price of damaged goods = $5 \times (1 - 0.40) = 5 \times 0.60 = 3$ 5. **Step 4: Calculate selling price of undamaged goods** 95% of goods are sold at $SP_2$ per unit: $$95 \times \frac{137.7}{100} = 130.815$$ 6. **Step 5: Calculate total selling price and profit/loss** Total selling price = selling price of undamaged goods + selling price of damaged goods $$= 130.815 + 3 = 133.815$$ Cost price = 100 Profit or loss = Total selling price - Cost price $$= 133.815 - 100 = 33.815$$ (profit) 7. **Step 6: Calculate profit percentage** $$\text{Profit \%} = \frac{33.815}{100} \times 100 = 33.815\%$$ **Final answer:** The trader makes an overall profit of approximately $33.82\%$.