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.
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Important Questions from Profit and Loss
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If the selling price of 7 articles is equal to the cost price of 6 articles, then what is the percentage loss?
An article when sold at a gain of 5%, yields Rs. 15 more than when sold at a loss of 5%. The cost price will be
What will be cost price of an item which when sold at the profit of 5% and at the loss of 5% the difference of selling prices be Rs. 60?
