Question : The first shirt is sold at twice the selling price of the second shirt. The first shirt is sold at 8% profit and the second shirt is sold at a 3% loss. What is the overall percentage profit on the shirts (Rounded off to two decimal places)?
Option 1: 4.86%
Option 2: 4.07%
Option 3: 4.60%
Option 4: 3.86%
Correct Answer: 4.07%
Solution : Let the selling price of the second shirt as \(x\). Then, the selling price of the first shirt is \(2x\). The cost price of the first shirt is \(\frac{2x}{1.08}\) (since it's sold at 8% profit), and the cost price of the second shirt is \(\frac{x}{0.97}\) (since it's sold at 3% loss). The total cost price is \(\frac{2x}{1.08} + \frac{x}{0.97}=2.8827x\), and the total selling price is \(2x + x = 3x\). The overall profit is the total selling price minus the total cost price, which is \(3x - 2.8827x=0.1172x\). The overall profit percentage = $\frac{\text{Overall profit}}{\text{Overall cost price}} \times 100$ The overall percentage profit = $\frac{0.1172x}{2.8827x} \times 100=4.065\%\approx4.07\%$ Hence, the correct answer is 4.07%.
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