Finding the Cost Price
Let the Cost Price (CP) be denoted by $C$.
Calculating Marked Price (MP)
- The item is marked 60% above the cost price.
- Marked Price, $MP = C \times (1 + \frac{60}{100}) = C \times (1 + 0.60) = 1.60C$.
Determining Selling Price (SP)
- A festival discount of 25% is offered on the marked price.
- Price after discount $= MP \times (1 - \frac{25}{100}) = 1.60C \times (1 - 0.25) = 1.60C \times 0.75 = 1.20C$.
- A cashback of Rs. 300 is given on the final selling price.
- Final Selling Price, $SP = (Price \ after \ discount) - 300 = 1.20C - 300$.
Relating SP, CP, and Profit
- The dealer makes a 10% profit on the cost price.
- Profit Amount $= C \times \frac{10}{100} = 0.10C$.
- The final selling price must cover the cost price plus the profit.
- $SP = CP + Profit = C + 0.10C = 1.10C$.
Solving for Cost Price (CP)
- Now, we equate the two expressions for the final selling price ($SP$):
- $1.20C - 300 = 1.10C$
- Rearrange the terms to solve for $C$:
- $1.20C - 1.10C = 300$
- $0.10C = 300$
- $C = \frac{300}{0.10}$
- $C = 3000$
Therefore, the cost price of the item is Rs. 3000.
Similar Questions
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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?
