Peter bought an item at 20% discount on its original price. He sold it with 40% increase on the price he bought it. The new sale price is by what percent more than the original price?

### Concept & Successive Percentages This problem evaluates percentage changes sequentially based on shifting base values (Original Price $\rightarrow$ Cost Price $\rightarrow$ Selling Price). $$ \text{SP} = \text{Original Price} \times (1 - \text{Discount}) \times (1 + \text{Markup}) $$ ### Step-by-Step Solution * Let the original price of the item be 100. * Peter bought it at a 20% discount. * Cost Price (CP) for Peter = $100 - (20\% \text{ of } 100) = 80$. * He sold it with a 40% increase on the price he bought it (CP). * Increase amount = $40\% \text{ of } 80 = 32$. * New Sale Price (SP) = $80 + 32 = 112$. * The difference between the new sale price and the original price = $112 - 100 = 12$. * Percentage increase over the original price = $\frac{12}{100} \times 100 = 12\%$. ### Exam Strategy & Shortcut Use the successive percentage change concept with a base of 100. Original = 100. After 20% discount: 80. After 40% markup on 80: $80 \times 1.4 = 112$. The change from 100 to 112 is exactly 12%. ### Common Pitfall Calculating the 40% markup on the original price (100) instead of the discounted price (80), which would incorrectly yield a sale price of 120 and a 20% profit. ### Final Answer Therefore, the correct answer is **12**.