A T-shirt bought for ₹ 50 is marked at 8 percent profit and then sold at a 10 percent sales discount on marked price. What is the selling price of the T-shirt?

### Concept & Markup and Discount The sequence of operations is to first increase the cost price by the markup percentage to find the marked price, and then decrease the marked price by the discount percentage to find the final selling price. $$ \text{Marked Price} = \text{Cost Price} \times \left(1 + \frac{\text{Markup \%}}{100}\right) $$ $$ \text{Selling Price} = \text{Marked Price} \times \left(1 - \frac{\text{Discount \%}}{100}\right) $$ ### Step-by-Step Solution * Cost Price (CP) of the T-shirt = ₹ 50. * It is marked at an $8\%$ profit margin. * Marked Price (MP) = $50 \times \left(1 + \frac{8}{100}\right) = 50 \times 1.08 = 54$. * It is then sold at a $10\%$ discount on the marked price. * Discount amount = $10\%$ of $54 = 5.4$. * Selling Price (SP) = MP - Discount = $54 - 5.4 = 48.6$. * Since ₹ 48.6 is not equal to ₹ 48, ₹ 50, or ₹ 52, the correct option is "None of these". ### Exam Strategy & Shortcut Use a single compound equation: $50 \times 1.08 \times 0.90$. $1.08 \times 0.90 = 0.972$. $50 \times 0.972 = \frac{100}{2} \times 0.972 = 48.6$. The options are integers, so "None of these" is immediately apparent. ### Common Pitfall A common mistake is thinking an $8\%$ markup followed by a $10\%$ discount results in a net $2\%$ loss on the original cost price ($50 \times 0.98 = 49$), ignoring that the discount is calculated on the higher marked price. ### Final Answer Therefore, the correct answer is **None of these**.