Question : An article is sold at a certain price. If it is sold at $33 \frac{1}{3}$% of this price, there is a loss of $33 \frac{1}{3}$%. What is the percentage profit if the article is sold at 80% of its original selling price?
Option 1: 60%
Option 2: 50%
Option 3: 70%
Option 4: 40%
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Correct Answer: 60%
Solution : Let $x$ be the original selling price. New selling price $= 33\frac{1}{3}$% of $x = \frac{x}{3}$ Let $y$ be the cost price. Loss $= 33\frac{1}{3}$% of $y = \frac{y}{3}$ ⇒ $y-\frac{x}{3} = \frac{y}{3}$ ⇒ $\frac{2y}{3} = \frac{x}{3}$ ⇒ Cost price $= y=\frac{x}{2}$ Now, selling price $= 80$% of $x = \frac{4x}{5}$ So, the profit percentage $=\frac{\frac{4x}{5}-\frac{x}{2}}{\frac{x}{2}}×100$ $=\frac{\frac{8x-5x}{10}}{\frac{x}{2}}×100$ $=\frac{3x × 2}{10×x}×100$ $=\frac{3}{5}×100$ $=60$% Hence, the correct answer is 60%.
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