Profit obtained on selling an article for Rs. 600 is equal to the loss incurred on selling the same article for Rs. 400. If selling price is Rs. 750, then what is the profit percentage?
50 percent
Understanding the Problem of Profit and Loss
The question involves a scenario where the profit made by selling an article at one price is equal to the loss incurred by selling the same article at a different price. We need to use this information to find the original cost price of the article. Once we know the cost price, we can calculate the profit percentage when the article is sold at a new selling price.
Finding the Cost Price When Profit Equals Loss
Let the Cost Price of the article be \( \text{CP} \).
When the article is sold for Rs. 600, there is a profit.
Profit = Selling Price - Cost Price
Profit = \( 600 - \text{CP} \)
When the article is sold for Rs. 400, there is a loss.
Loss = Cost Price - Selling Price
Loss = \( \text{CP} - 400 \)
According to the problem, the profit obtained is equal to the loss incurred.
Profit = Loss
\( 600 - \text{CP} = \text{CP} - 400 \)
Calculating the Cost Price
We can solve the equation above to find the value of \( \text{CP} \).
\( 600 - \text{CP} = \text{CP} - 400 \)
Add \( \text{CP} \) to both sides:
\( 600 = \text{CP} + \text{CP} - 400 \)
\( 600 = 2\text{CP} - 400 \)
Add 400 to both sides:
\( 600 + 400 = 2\text{CP} \)
\( 1000 = 2\text{CP} \)
Divide both sides by 2:
\( \text{CP} = \frac{1000}{2} \)
\( \text{CP} = 500 \)
So, the Cost Price of the article is Rs. 500.
Calculating Profit Percentage for New Selling Price
Now, the article is sold for Rs. 750.
New Selling Price \( (\text{SP}_{\text{new}}) = 750 \)
Cost Price \( (\text{CP}) = 500 \)
Since the Selling Price (750) is greater than the Cost Price (500), there is a profit.
Profit = \( \text{SP}_{\text{new}} - \text{CP} \)
Profit = \( 750 - 500 \)
Profit = \( 250 \)
The profit percentage is calculated using the formula:
Profit Percentage \( = \left( \frac{\text{Profit}}{\text{CP}} \right) \times 100 \)
Profit Percentage \( = \left( \frac{250}{500} \right) \times 100 \)
Profit Percentage \( = \left( \frac{1}{2} \right) \times 100 \)
Profit Percentage \( = 0.5 \times 100 \)
Profit Percentage \( = 50 \)
The profit percentage is 50 percent.
Summary of Calculations
| Scenario | Selling Price (Rs.) | Cost Price (Rs.) | Result (Profit/Loss) | Calculation |
|---|---|---|---|---|
| 1 | 600 | 500 | Profit | \(600 - 500 = 100\) |
| 2 | 400 | 500 | Loss | \(500 - 400 = 100\) |
| New Scenario | 750 | 500 | Profit | \(750 - 500 = 250\) |
| Calculation | Value |
|---|---|
| Cost Price (CP) | 500 |
| Profit (New Scenario) | 250 |
| Profit Percentage | \( \left( \frac{250}{500} \right) \times 100 = 50\% \) |
Revision Table: Key Concepts in Profit and Loss
| Concept | Definition | Formula |
|---|---|---|
| Cost Price (CP) | The price at which an article is purchased. | N/A |
| Selling Price (SP) | The price at which an article is sold. | N/A |
| Profit | Occurs when SP > CP. | Profit = SP - CP |
| Loss | Occurs when CP > SP. | Loss = CP - SP |
| Profit Percentage | Profit calculated as a percentage of CP. | \( \left( \frac{\text{Profit}}{\text{CP}} \right) \times 100 \) |
| Loss Percentage | Loss calculated as a percentage of CP. | \( \left( \frac{\text{Loss}}{\text{CP}} \right) \times 100 \) |
Additional Information: Solving Equal Profit and Loss Problems
In problems where the profit from one selling price equals the loss from another selling price for the same article, the Cost Price (CP) is always the average of the two selling prices.
Let the two selling prices be \( \text{SP}_1 \) (resulting in profit) and \( \text{SP}_2 \) (resulting in loss), such that Profit = Loss.
\( \text{SP}_1 - \text{CP} = \text{CP} - \text{SP}_2 \)
\( \text{SP}_1 + \text{SP}_2 = 2\text{CP} \)
\( \text{CP} = \frac{\text{SP}_1 + \text{SP}_2}{2} \)
In this specific problem, \( \text{SP}_1 = 600 \) and \( \text{SP}_2 = 400 \).
\( \text{CP} = \frac{600 + 400}{2} = \frac{1000}{2} = 500 \)
This confirms our calculated Cost Price using the average method, making the calculation quicker for similar problems.
Important Questions from Profit and Loss
Rohit buys 8 pens and 4 pencils for Rs. 2400. He sells pencils at a profit of 20 percent and pens at the loss of 10 percent. If his overall profit is Rs. 240, then what is the sum of the cost price of one pen and one pencil?
A man sells a car to his friend at the loss of 10 %; who in return sells it for Rs. 54000 making a profit of 20 %. What was the initial value of the car?
An article was sold at a loss of 24%. If it were sold for Rs. 1,596 more, then there would have been a gain of 18%, The cost price of the article is:
The cost price of an article is Rs.6,450. If it sold at a profit 16%, how much would be its selling price?
If the selling price of 7 articles is equal to the cost price of 6 articles, then what is the percentage loss?
