Question : 15% of the marked price of an item is equal to 25% of its cost price. If a discount of 25% is given on the sale of the item, then what will be the profit percentage?
Option 1: 22.5%
Option 2: 20%
Option 3: 17.5%
Option 4: 25%
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Correct Answer: 25%
Solution : Given: 15% of the marked price of an item is equal to 25% of its cost price. ⇒ $0.15\ MP = 0.25\ CP$ ⇒ $\frac{MP}{CP} = \frac{25}{15}$ ⇒ $\frac{MP}{CP} = \frac{5}{3}$ Use the formula, $\frac{CP}{MP}=\frac{100– D}{100+P}$ where $CP$, $MP$, $D$, and $P$ are the cost price, marked price, discount percentage, and profit percentage, respectively. According to the question, $\frac{3}{5}=\frac{100– 25}{100+P}$ ⇒ $\frac{3}{5}=\frac{75}{100+P}$ ⇒ $100+P=125$ ⇒ $P=125-100$ ⇒ $P=25\%$ Hence, the correct answer is 25%.
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