The marked price is 10% higher than the cost price. A discount of 10% is given on the marked price. In this kind of sale, the seller

### Concept & Formula When an item's price is first increased by $x\%$ and then decreased by the same $x\%$, there is always a net decrease (loss). The net change is given by the formula: $$Net \% Change = \frac{-x^2}{100}$$ ### Step-by-Step Solution 1. Let the Cost Price (CP) be $100$. 2. The Marked Price (MP) is $10\%$ higher than CP: $$MP = 100 + 10 = 110$$ 3. A discount of $10\%$ is given on the MP: Discount = $10\%$ of $110 = 11$ Selling Price (SP) = $110 - 11 = 99$ 4. Calculate the net loss: $$Loss = CP - SP = 100 - 99 = 1$$ $$Loss \% = \left(\frac{1}{100}\right) \times 100\% = 1\%$$ ### Exam Strategy & Shortcut Use the direct successive percentage formula: $+10\%$ (markup) and $-10\%$ (discount). Net change = $+10 - 10 - \frac{10 \times 10}{100} = -1\%$ The negative sign indicates a loss of $1\%$. ### Common Pitfall Assuming that a $10\%$ markup followed by a $10\%$ discount cancels each other out, resulting in "no loss, no gain". The discount is applied on the higher marked price, leading to an overall loss. ### Final Answer Therefore, the correct answer is **loses 1%**.