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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Question : A dealer marks his goods at 15% above the cost price and allows a discount of 5% for cash payment. His profit percentage is:
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