Question : If 25% discount is given on an article, then there will be a loss of 15%. If the article is sold at its marked price, then what will the profit percentage be? [Give your answer correct to 2 decimal places.]
Option 1: 15.66%
Option 2: 12.66%
Option 3: 13.33%
Option 4: 10.22%
Correct Answer: 13.33%
Solution :
Discount percentage (d) = 25%
Loss percentage (l) = 15%
$\frac{\text{Marked Price}}{\text{Cost Price}} = \frac{100 - \text{loss%}}{100 - \text{discount%}}$
Using the formula
$\frac{\text{Marked Price}}{\text{Cost Price}} = \frac{100 - 15}{100 - 25}$
⇒ $\frac{\text{MP}}{\text{CP}} = \frac{85}{75}$
⇒ $\frac{\text{Marked Price}}{\text{Cost Price}} = \frac{17}{15}$
Now, the Selling Price (SP) is equal to the Marked Price (MP) as no discount is there to avail. The cost Price is CP.
Let MP = SP = 17 and CP = 15
Profit = 17 - 15 = 2
Profit% = $\frac{2}{15} \times 100$ = 13.33%
$\therefore$ The profit percentage is 13.33%.
Hence, the correct answer is 13.33%.
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