A shop owner marks up the price of an item by 25% above the cost price. To attract customers, he decides to offer a discount of 10% on the marked price. What is the overall percent... A shop owner marks up the price of an item by 25% above the cost price. To attract customers, he decides to offer a discount of 10% on the marked price. What is the overall percentage profit the shop owner makes on each item?
Understand the Problem
The question is asking to calculate overall profit percentage after a markup and a discount. We need to determine the final selling price relative to the original cost price to find the profit percentage.
Answer
$8\%$
Answer for screen readers
The overall profit percentage is $8%$.
Steps to Solve
- Assume a cost price
To make calculations easier, assume the cost price of the item is $100.
- Calculate the price after the markup
A 20% markup on the cost price means the price is increased by 20% of $100:
Markup amount = $0.20 \times $100 = $20$ Price after markup = $$100 + $20 = $120$
- Calculate the price after the discount
A 10% discount on the marked-up price means the price is reduced by 10% of $120:
Discount amount = $0.10 \times $120 = $12$ Price after discount = $$120 - $12 = $108$
- Calculate the overall profit
The overall profit is the difference between the final selling price and the original cost price:
Profit = $$108 - $100 = $8$
- Calculate the profit percentage
The profit percentage is the profit divided by the original cost price, expressed as a percentage:
Profit percentage = $\frac{$8}{$100} \times 100% = 8%$
The overall profit percentage is $8%$.
More Information
The problem can be solved without assuming a cost price. If the cost price = $C$, after markup, Selling Price = $1.2C$. After discount, Selling Price = $0.9 \times 1.2C$ = $1.08C$. Profit = $1.08C - C= 0.08C$ Profit Percentage = $\frac{0.08C}{C} \times 100$ = $8%$
Tips
A common mistake is to calculate the discount based on the original cost instead of the marked-up price. This would lead to an incorrect final selling price and therefore an incorrect profit percentage. Another error may arise from adding/subtracting percentages directly, without converting them to the cost's corresponding value.
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