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
-
Assume Cost Price (CP): Let the Cost Price be $100.
-
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 = $100 + \$8 = \$108$.
-
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: $\$108 = 0.90 \times MP$ $MP = \frac{\$108}{0.90} = \$120$.
-
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
By selling an article for Rs. 2,200, a profit of 10% is earned. If the same article is sold for Rs. 2,600, then what will be the gain percentage?
By selling an article for Rs. 640, a person loses 15% of its selling price. At what price (in Rs.) should he sell it to gain 15% on its cost price?
The selling prices of articles A and B are the same. A is sold at a profit of 28 percent and B is sold at a loss of 24 percent. If the total selling price of the both articles is Rs. 48640, then what is the cost price of A and B, respectively ?
The cost price of an article is Rs. 2800. Profit as a percentage of selling price is 20 percent. What is the actual profit (in Rs.) ?
A trader bought 640 kg of rice. He sold a part of rice at 20% profit and the rest at 5% loss. He earned a profit of 15% in the entire transaction. What is the quantity (in kg) of rice that he sold at 5% loss?
