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 ?
Rs. 19000, Rs. 32000
Finding Cost Price when Selling Price is Same
This problem involves calculating the cost price of two articles, Article A and Article B, given their selling prices are equal, one is sold at a profit, and the other at a loss. We are also given the total selling price of both articles.
Understanding the Given Information
- Selling price of Article A = Selling price of Article B. Let's denote this common selling price by \(SP\).
- Total selling price of both articles = Rs. 48640.
- Article A is sold at a profit of 28 percent.
- Article B is sold at a loss of 24 percent.
- We need to find the cost price of Article A (\(CP_A\)) and Article B (\(CP_B\)).
Step-by-Step Solution
Step 1: Calculate the individual selling price of each article.
Since the selling price of Article A and Article B are the same, and their total selling price is Rs. 48640, we can find the selling price of one article by dividing the total selling price by 2.
Total Selling Price = \(SP_A + SP_B = 48640\)
Since \(SP_A = SP_B\), we have \(2 \times SP = 48640\).
Therefore, the selling price of each article is:
\(SP = \frac{48640}{2} = 24320\)
So, \(SP_A = Rs. 24320\) and \(SP_B = Rs. 24320\).
Step 2: Calculate the Cost Price of Article A.
Article A is sold at a profit of 28 percent. The selling price (\(SP_A\)) is related to the cost price (\(CP_A\)) by the formula:
\(SP_A = CP_A \times (1 + \text{Profit Percentage})\)
\(SP_A = CP_A \times (1 + \frac{28}{100})\)
\(24320 = CP_A \times (1 + 0.28)\)
\(24320 = CP_A \times 1.28\)
To find \(CP_A\), we rearrange the formula:
\(CP_A = \frac{24320}{1.28}\)
Performing the division:
\(CP_A = 19000\)
So, the cost price of Article A is Rs. 19000.
Step 3: Calculate the Cost Price of Article B.
Article B is sold at a loss of 24 percent. The selling price (\(SP_B\)) is related to the cost price (\(CP_B\)) by the formula:
\(SP_B = CP_B \times (1 - \text{Loss Percentage})\)
\(SP_B = CP_B \times (1 - \frac{24}{100})\)
\(24320 = CP_B \times (1 - 0.24)\)
\(24320 = CP_B \times 0.76\)
To find \(CP_B\), we rearrange the formula:
\(CP_B = \frac{24320}{0.76}\)
Performing the division:
\(CP_B = 32000\)
So, the cost price of Article B is Rs. 32000.
Conclusion
The cost price of Article A is Rs. 19000 and the cost price of Article B is Rs. 32000.
These values match the required cost prices of A and B, respectively.
Revision Table: Key Formulas
| Concept | Formula |
|---|---|
| Profit Percentage | \(\frac{\text{Selling Price} - \text{Cost Price}}{\text{Cost Price}} \times 100\%\) |
| Loss Percentage | \(\frac{\text{Cost Price} - \text{Selling Price}}{\text{Cost Price}} \times 100\%\) |
| Selling Price (with Profit) | \(\text{Cost Price} \times (1 + \frac{\text{Profit Percentage}}{100})\) |
| Selling Price (with Loss) | \(\text{Cost Price} \times (1 - \frac{\text{Loss Percentage}}{100})\) |
| Cost Price (from SP & Profit %) | \(\frac{\text{Selling Price}}{1 + \frac{\text{Profit Percentage}}{100}}\) |
| Cost Price (from SP & Loss %) | \(\frac{\text{Selling Price}}{1 - \frac{\text{Loss Percentage}}{100}}\) |
Additional Information: Profit and Loss Basics
Profit and loss are fundamental concepts in commercial arithmetic. They describe the financial outcome of a transaction.
- Cost Price (CP): The price at which an article is purchased.
- Selling Price (SP): The price at which an article is sold.
- Profit: Occurs when SP > CP. Profit = SP - CP.
- Loss: Occurs when CP > SP. Loss = CP - SP.
- Profit Percentage: Calculated on the Cost Price. \(\text{Profit } \% = \frac{\text{Profit}}{\text{CP}} \times 100\).
- Loss Percentage: Calculated on the Cost Price. \(\text{Loss } \% = \frac{\text{Loss}}{\text{CP}} \times 100\).
Understanding these basics is crucial for solving problems involving profit and loss calculations, like the one discussed where selling prices are equal but the cost prices differ due to different profit/loss percentages.
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