Solution: Marked Price Markup Percentage Calculation
This problem requires calculating the markup percentage needed on the cost price to achieve a specific profit after applying a discount. We need to find how much the marked price (MP) should exceed the cost price (CP) to ensure a $10\%$ profit when a $5\%$ discount is given on the MP.
Steps to Calculate Markup Percentage
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Assume Cost Price (CP): Let the Cost Price be $100$. This simplifies percentage calculations.
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Determine Target Selling Price (SP): A profit of $10\%$ is desired. SP = CP + (Profit percentage of CP) SP = $100 + (10\% \times 100) = 100 + 10 = 110$. The target Selling Price is $110$.
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Relate Selling Price (SP) to Marked Price (MP): A discount of $5\%$ is offered on the card payment (which is based on the Marked Price). This means the Selling Price is $95\%$ of the Marked Price. SP = MP $\times (1 - \frac{\text{Discount}}{100})$ $110 = \text{MP} \times (1 - \frac{5}{100})$ $110 = \text{MP} \times (1 - 0.05)$ $110 = \text{MP} \times 0.95$
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Calculate Marked Price (MP): Rearrange the formula to find MP. MP = $\frac{110}{0.95} = \frac{11000}{95} = \frac{2200}{19}$. The Marked Price is $\frac{2200}{19}$.
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Calculate Markup Amount: The markup is the difference between the Marked Price and the Cost Price. Markup Amount = MP - CP Markup Amount = $\frac{2200}{19} - 100 = \frac{2200 - (100 \times 19)}{19} = \frac{2200 - 1900}{19} = \frac{300}{19}$.
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Calculate Markup Percentage: The markup percentage is calculated based on the Cost Price. Markup Percentage = $(\frac{\text{Markup Amount}}{CP}) \times 100$ Markup Percentage = $(\frac{300/19}{100}) \times 100 = \frac{300}{19}\%$.
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Convert to Mixed Fraction: Convert the improper fraction $\frac{300}{19}$ to a mixed number. $300 \div 19 = 15$ with a remainder of $15$. So, $\frac{300}{19} = 15 \frac{15}{19}$.
Therefore, the marked price should be $15 \frac{15}{19}\%$ above the cost price.
Similar Questions
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Important Questions from Profit and Loss
Rohit buys 8 pens and 4 pencils for Rs. 2400. He sells pencils at a profit of 20 percent and pens at the loss of 10 percent. If his overall profit is Rs. 240, then what is the sum of the cost price of one pen and one pencil?
A man sells a car to his friend at the loss of 10 %; who in return sells it for Rs. 54000 making a profit of 20 %. What was the initial value of the car?
By selling a horse for Rs. 670, a tradesman would lose 5%. At what price must he sell it to gain 5%?
An article was sold at a loss of 24%. If it were sold for Rs. 1,596 more, then there would have been a gain of 18%, The cost price of the article is:
The cost price of an article is Rs.6,450. If it sold at a profit 16%, how much would be its selling price?
