Cost Price Calculation for Frocks
This solution details the steps to calculate the cost price of the first frock, given the total purchase price, individual selling conditions (loss percentage for the first frock and gain percentage for the second), and the overall break-even outcome.
Information Summary
- Total Cost Price (CPTotal): ₹1,200
- Frock 1: Sold at a 7% loss. Its cost price is CP1.
- Frock 2: Sold at a 23% gain. Its cost price is CP2.
- Overall Result: No profit, no loss. This implies Total Selling Price (SPTotal) = CPTotal.
Formulating Equations
Based on the information provided, we can establish the following relationships:
- Sum of individual cost prices: CP1 + CP2 = ₹1,200
- Selling Price of Frock 1 (SP1): SP1 = CP1 × (1 - 7/100) = CP1 × 0.93
- Selling Price of Frock 2 (SP2): SP2 = CP2 × (1 + 23/100) = CP2 × 1.23
- Total Selling Price equals Total Cost Price: SP1 + SP2 = ₹1,200
Solving for CP1
Substitute the expressions for SP1 and SP2 into the total selling price equation:
$ ( \text{CP}_{1} \times 0.93 ) + ( \text{CP}_{2} \times 1.23 ) = 1200 $
Use the relationship CP2 = 1200 - CP1 from the first equation and substitute it:
$ ( \text{CP}_{1} \times 0.93 ) + ( (1200 - \text{CP}_{1}) \times 1.23 ) = 1200 $
Expand and rearrange the equation to solve for CP1:
$ 0.93 \times \text{CP}_{1} + 1476 - 1.23 \times \text{CP}_{1} = 1200 $
Combine terms involving CP1:
$ (0.93 - 1.23) \times \text{CP}_{1} = 1200 - 1476 $
$ -0.30 \times \text{CP}_{1} = -276 $
Calculate the value of CP1:
$ \text{CP}_{1} = \frac{-276}{-0.30} = \frac{276}{0.30} $
$ \text{CP}_{1} = 920 $
Conclusion
The cost price (in ₹) of the first frock is 920.
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?
