By selling two articles, each for Rs. 270, a shopkeeper gains the cost price of one article. The cost price of one article and the profit percentage, respectively, are:
Rs. 180 and 50%
Understanding the Problem: Profit and Loss Calculation
The question asks us to find the cost price of a single article and the overall profit percentage made by a shopkeeper. We are given that two articles are sold, each at a specific selling price, and the total profit earned is equal to the cost price of one of these articles.
Setting Up the Calculation
Let's denote the cost price of one article as \(CP\). Since two articles are sold, and we assume they are identical in terms of cost for the profit calculation described:
- Cost Price of the first article = \(CP\)
- Cost Price of the second article = \(CP\)
- Total Cost Price of two articles = \(CP + CP = 2 \times CP\)
We are given the selling price of each article:
- Selling Price of the first article = Rs. 270
- Selling Price of the second article = Rs. 270
- Total Selling Price of two articles = Rs. \(270 + 270 = 540\)
The problem states that the total profit gained is equal to the cost price of one article.
- Total Profit = Cost Price of one article = \(CP\)
The basic formula for profit is:
\(\text{Total Profit} = \text{Total Selling Price} - \text{Total Cost Price}\)
Solving for the Cost Price
Now, we can substitute the values we have into the profit formula:
\(CP = 540 - (2 \times CP)\)
To find the value of \(CP\), we need to rearrange the equation. Add \(2 \times CP\) to both sides:
\(CP + 2 \times CP = 540\)
\(3 \times CP = 540\)
Now, divide both sides by 3:
\(CP = \frac{540}{3}\)
\(CP = 180\)
So, the cost price of one article is Rs. 180.
Calculating the Profit Percentage
The profit percentage is calculated on the total cost price. We know:
- Total Profit = Rs. 180 (which is equal to the cost price of one article, as stated in the problem)
- Total Cost Price = \(2 \times CP = 2 \times 180 = \text{Rs. } 360\)
The formula for profit percentage is:
\(\text{Profit Percentage} = \left( \frac{\text{Total Profit}}{\text{Total Cost Price}} \right) \times 100\%\)
Substitute the values:
\(\text{Profit Percentage} = \left( \frac{180}{360} \right) \times 100\%\)
\(\text{Profit Percentage} = \left( \frac{1}{2} \right) \times 100\%\)
\(\text{Profit Percentage} = 50\%\)
Summary of Findings
Based on our calculations:
- The cost price of one article is Rs. 180.
- The profit percentage is 50%.
We can verify this:
- Cost of 2 articles = \(2 \times 180 = 360\)
- Selling price of 2 articles = \(2 \times 270 = 540\)
- Total Profit = \(540 - 360 = 180\)
- This profit (Rs. 180) is indeed equal to the cost price of one article (Rs. 180). The condition in the question is met.
| Metric | Value |
|---|---|
| Selling Price per Article | Rs. 270 |
| Total Selling Price (2 articles) | Rs. 540 |
| Cost Price per Article (calculated) | Rs. 180 |
| Total Cost Price (2 articles) | Rs. 360 |
| Total Profit (calculated) | Rs. 180 |
| Profit as % of Total Cost Price | 50% |
Final Answer
The cost price of one article is Rs. 180 and the profit percentage is 50%.
Revision Table: Key Concepts in Profit and Loss
| Term | Definition | Formula |
|---|---|---|
| Cost Price (CP) | The price at which an article is bought. | - |
| Selling Price (SP) | The price at which an article is sold. | - |
| Profit | When SP > CP. The excess amount received from selling an article. | Profit = SP - CP |
| Loss | When SP < CP. The deficit amount from selling an article. | Loss = CP - SP |
| Profit Percentage | Profit calculated as a percentage of the Cost Price. | \(\text{Profit Percentage} = \left( \frac{\text{Profit}}{\text{CP}} \right) \times 100\%\) |
| Loss Percentage | Loss calculated as a percentage of the Cost Price. | \(\text{Loss Percentage} = \left( \frac{\text{Loss}}{\text{CP}} \right) \times 100\%\) |
Additional Information: Handling Multiple Articles
When dealing with multiple articles in profit and loss problems, it's often helpful to consider the total cost price and the total selling price. The total profit or loss is the difference between the total selling price and the total cost price.
If articles are identical in cost price, you can use the cost price of a single article (\(CP\)) to find the total cost price (\(n \times CP\) for \(n\) articles). If the selling price is the same for each article, the total selling price is \(n \times SP\).
Profit or loss percentage is typically calculated on the total cost price unless specified otherwise.
In this problem, equating the total profit (\(\text{Total SP} - \text{Total CP}\)) to the cost price of one article (\(CP\)) was the key step to finding the unknown \(CP\).
Similar Questions
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Important Questions from Successive Selling
- During a sale 35% of the goods are sold at 22% profit, 40% of the remaining goods are sold at 37% profit and the still remaining goods are sold at a loss of 38%. If there is an overall profit of x%, then what is the value of x?
- A dealer buys two articles X and Y for ₹1,000 each. He marks each of them at the same price. He sells X by giving two successive discounts of 15% and 30% and still earns ₹337 as profit. If he sells Y at a single discount of 49%, then what is the profit percentage on Y?
- Find the single equivalent discount (rounded off to two decimal places) for successive discounts of 18%, 6% and 25%.
A shopkeeper marks the price of three identical articles, first, 60% above the Cost Price; second, 45% above the Cost Price and the third, 40% above the cost price. If he gives discount of 25% on first article, 20% on the second article and 15% on the third one, what is his overall profit percentage?
A dealer bought a six-seater Dining Table after getting successive discounts of 15% and 12%. Thereafter, he spent 10% on transport, etc. and finally sold it for Rs. 24,169.75, thereby earning a profit of 25%. What was the marked price of the Dining Table?
