If the selling price of 7 articles is equal to the cost price of 8 articles, then what is the profit percentage (correct to one decimal place)?
14.3%
Calculating Profit Percentage: Selling Price vs Cost Price
This question involves calculating the profit percentage based on a relationship between the selling price (SP) and the cost price (CP) of a certain number of articles. Understanding the core definitions of cost price, selling price, profit, and profit percentage is key to solving this type of problem.
Understanding the Relationship Given
The problem states that the selling price of 7 articles is equal to the cost price of 8 articles. Let's denote:
- \( CP_{article} \) = Cost Price of one article
- \( SP_{article} \) = Selling Price of one article
According to the problem statement, the total selling price of 7 articles is equal to the total cost price of 8 articles. We can write this as an equation:
\( 7 \times SP_{article} = 8 \times CP_{article} \)
Finding the Relationship Between SP and CP per Article
From the equation above, we can express the selling price of one article in terms of the cost price of one article:
\( SP_{article} = \frac{8}{7} \times CP_{article} \)
This equation tells us that the selling price of one article is greater than its cost price (\( \frac{8}{7} > 1 \)), indicating that there is a profit.
Calculating the Profit
Profit is defined as the difference between the selling price and the cost price of an article. For one article, the profit is:
\( \text{Profit per article} = SP_{article} - CP_{article} \)
Substitute the expression for \( SP_{article} \):
\( \text{Profit per article} = \frac{8}{7} \times CP_{article} - CP_{article} \)
\( \text{Profit per article} = \left(\frac{8}{7} - 1\right) \times CP_{article} \)
\( \text{Profit per article} = \left(\frac{8}{7} - \frac{7}{7}\right) \times CP_{article} \)
\( \text{Profit per article} = \frac{1}{7} \times CP_{article} \)
Determining the Profit Percentage
The profit percentage is calculated using the formula:
\( \text{Profit Percentage} = \left( \frac{\text{Profit}}{\text{Cost Price}} \right) \times 100 \)
Using the profit per article and the cost price per article:
\( \text{Profit Percentage} = \left( \frac{\frac{1}{7} \times CP_{article}}{CP_{article}} \right) \times 100 \)
The \( CP_{article} \) terms cancel out:
\( \text{Profit Percentage} = \frac{1}{7} \times 100 \)
\( \text{Profit Percentage} = \frac{100}{7} \)
Calculating the Final Percentage
Now, we calculate the numerical value of \( \frac{100}{7} \):
\( \frac{100}{7} \approx 14.2857... \)
The question asks for the profit percentage correct to one decimal place. Rounding 14.2857... to one decimal place gives 14.3%.
Therefore, the profit percentage is approximately 14.3%.
Revision Table: Key Formulas
| Concept | Formula |
|---|---|
| Profit | Selling Price - Cost Price |
| Loss | Cost Price - Selling Price |
| Profit Percentage | \( \left( \frac{\text{Profit}}{\text{Cost Price}} \right) \times 100 \) |
| Loss Percentage | \( \left( \frac{\text{Loss}}{\text{Cost Price}} \right) \times 100 \) |
Additional Information on Profit and Loss Concepts
Profit and loss are fundamental concepts in business and commerce. They describe the financial outcome of buying and selling goods or services.
- Cost Price (CP): This is the price at which an article is bought.
- Selling Price (SP): This is the price at which an article is sold.
- Profit: Occurs when SP > CP. It is the gain made from a transaction.
- Loss: Occurs when SP < CP. It is the deficit incurred in a transaction.
- Percentage Calculation Basis: Both profit percentage and loss percentage are typically calculated on the cost price unless otherwise specified. This provides a consistent basis for comparing profitability or loss across different items or transactions.
Understanding these basics is crucial for solving problems involving percentages in commercial mathematics.
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