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
Ram bought a chair at 35% discount on its market price, Had Ram got no discount, he would have had to pay ₹245 more. How much did Ram pay for the chair?
A shopkeeper bought an item for Rs. 4,500 and sold it at a loss of 5%. From this money, he bought another item and sold it at a profit of 10%. What is his overall profit?
A man sells two articles at Rs. 9,180 each. He gains 8% on one article and loses 15% on the other. His overall profit or loss is:
A shopkeeper selling an article for ₹46 loses 8%. In order to gain 6%, what should be the selling price of the article?
Rahul purchased 80 items from the market. 25% items of the total items were defective and the remaining items were sold at 50% profit. What will be the overall profit percentage?
