Question : A person marks his goods $x$% above the cost price and allows a discount of 12% on the marked price. If his profit is 10%, the difference between $x$% and the profit percentage is:
Option 1: 15%
Option 2: 18%
Option 3: 13%
Option 4: 10%
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Correct Answer: 15%
Solution :
Let the Cost price (CP) be $100$.
Then, the marked price (MP) is $100 + \frac{100 × x}{100} = 100+x$.
Discount is $12$% and profit is $10$%.
Place the values in the formula, $\frac{MP}{CP} = \frac{100+\text{Profit%}}{100–\text{Discount%}}$,
$⇒\frac{100+x}{100} = \frac{100+10}{100–12}$
$⇒\frac{100+x}{100} = \frac{110}{88}$
$⇒100+x = \frac{110×100}{88} = 125$
$⇒x = 125–100$
$⇒x = 25$%
The difference between $x$% and the profit percentage = $25$% – $10$% = $15$%
Hence, the correct answer is 15%.
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