Marked Price Hike Calculation
The goal is to find the percentage increase from the cost price (CP) to the marked price (MP) required to achieve a specific profit after a discount.
Step-by-Step Solution
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Assume Cost Price (CP): Let the Cost Price be $100.
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Calculate Selling Price (SP): A profit of 8% is desired. Profit = $8\%$ of $100 = \frac{8}{100} \times 100 = \$8$ Selling Price (SP) = CP + Profit = $100 + \$8 = \$108$.
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Calculate Marked Price (MP): A discount of 10% is allowed on the Marked Price. The Selling Price is 90% of the Marked Price (since 100% - 10% = 90%). $SP = MP - (10\% \text{ of } MP)$ $SP = MP - 0.10 \times MP$ $SP = 0.90 \times MP$ Substituting the SP: $\$108 = 0.90 \times MP$ $MP = \frac{\$108}{0.90} = \$120$.
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Calculate Percentage Hike: The hike is the difference between the Marked Price and the Cost Price. Hike = MP - CP = $\$120 - \$100 = \$20$. Percentage Hike = $\frac{\text{Hike}}{\text{CP}} \times 100$ Percentage Hike = $\frac{\$20}{\$100} \times 100 = 20\%$.
Therefore, the marked price must be hiked by 20% from the cost price.
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?
The cost price of an article is Rs.6,450. If it sold at a profit 16%, how much would be its selling price?
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?
