Question : If 80% of total articles are sold at a loss of 25% and the remaining articles are sold at a profit of 20%, what will be the overall loss percentage?
Option 1: 20%
Option 2: 18%
Option 3: 16%
Option 4: 22%
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Correct Answer: 16%
Solution : Let Rs. $x$ be the cost price of each object. Then, the cost price of 80% of the articles = 80% of $x$ = $\frac{4}{5}x$ However, a 25% loss is experienced = 25% of $\frac{4}{5}x=\frac{1}{4}\times \frac{4x}{5}=\frac{x}{5}$ The selling price of 80% of the articles $=\frac{4}{5}x-\frac{1}{5}x=\frac{3x}{5}$ The cost price of the remaining articles $=x-\frac{4}{5}x=\frac{x}{5}$ However, a 20% profit exists = 20% of $\frac{1}{5}x$ = $\frac{x}{25}$ The selling price of the remaining items $=\frac{1}{5}x+\frac{1}{25}x=\frac{6x}{25}$ The selling price of all articles $=\frac{3}{5}x+\frac{6}{25}x=\frac{21x}{25}$ The total loss $=x- \frac{21}{25}x=\frac{4x}{25}$ The total loss percentage = $\frac{\text{Total loss}}{\text{Cost price}}×100=\frac{\frac{4x}{25}}{x}\times 100=16$% Hence, the correct answer is 16%.
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