Question : An article was sold at a certain price. Had it been sold at $\frac{4}{5}$ of that price, there would have been a loss of 10%. At what profit percentage was the article sold initially?
Option 1: 10.5
Option 2: 15
Option 3: 12.5
Option 4: 10
Correct Answer: 12.5
Solution :
Let the initial selling price = 100
New selling price = $\frac{4}{5} × 100$ = 80
So, according to the question,
cost price = $\frac{100}{90}$ × 80
= $\frac{800}{9}$
Profit percentage = $\frac{\text{selling price - cost price}}{\text{cost price}}$ × 100
= $\frac{100 - \frac{800}{9}}{\frac{800}{9}}$ × 100
= $\frac{100}{800}$ × 100
= 12.5%
Hence, the correct answer is 12.5.
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