A trader marked the selling price of an article at 10% above the cost price. At the time of selling, he allows certain discount and suffers a loss of 1%. He allowed a discount of

### Concept & Base Values for Percentage Set a base value of 100 for the Cost Price to easily map out the Marked Price, Selling Price, and track the percentage differences without complex algebra. ### Step-by-Step Solution - Let the Cost Price (CP) of the article be Rs. 100. - The trader marks the price $10\%$ above the CP. - Marked Price (MP) = $100 + 10\% \text{ of } 100 = \text{Rs. } 110$. - During the sale, there is an overall loss of $1\%$. - Selling Price (SP) = $\text{CP} - 1\% \text{ of } \text{CP} = 100 - 1 = \text{Rs. } 99$. - The discount is given on the Marked Price to arrive at the Selling Price. - Discount Amount = $\text{MP} - \text{SP} = 110 - 99 = \text{Rs. } 11$. - Discount Percentage = $(\frac{\text{Discount Amount}}{\text{MP}}) \times 100$. - Discount Percentage = $(\frac{11}{110}) \times 100 = \frac{1}{10} \times 100 = 10\%$. ### Exam Strategy & Shortcut Let CP = 100. Mark up is $+10$, so MP = 110. Final result is a $-1$ loss, so SP = 99. The drop from 110 to 99 is 11. $\frac{11}{110}$ is exactly $\frac{1}{10}$, which equals a $10\%$ discount. This can be calculated mentally in seconds. ### Common Pitfall Calculating the discount percentage on the Cost Price (100) instead of the Marked Price (110). A discount of 11 on a base of 100 would be $11\%$, which is a trap option. Discounts are always calculated on MP. ### Final Answer Therefore, the correct answer is **10%**.