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?
30%
Understanding Profit and Loss Calculations
This problem involves calculating the profit percentage when an article is sold at different prices. We are given the selling price and profit percentage for one scenario and the selling price for a second scenario, and we need to find the profit percentage in the second case. To solve this, we first need to determine the original cost price of the article, which remains constant.
Step-by-Step Solution to Find Gain Percentage
Let's break down the problem into clear steps:
- Find the Cost Price (CP) of the article.
We know the first selling price (SP<sub>1</sub>) and the profit percentage (Profit%<sub>1</sub>) earned at this price. The formula relating Selling Price, Cost Price, and Profit Percentage is:
\( \text{SP} = \text{CP} \times \left(1 + \frac{\text{Profit%}}{100}\right) \)
We can rearrange this formula to find the Cost Price:
\( \text{CP} = \frac{\text{SP}}{1 + \frac{\text{Profit%}}{100}} \)
Given:
- SP<sub>1</sub> = Rs. 2,200
- Profit%<sub>1</sub> = 10%
Substitute these values into the formula:
\( \text{CP} = \frac{2200}{1 + \frac{10}{100}} = \frac{2200}{1 + 0.10} = \frac{2200}{1.10} \)
Calculating the value:
\( \text{CP} = 2000 \)
So, the Cost Price of the article is Rs. 2,000.
- Calculate the Profit when selling at the new price.
The new selling price (SP<sub>2</sub>) is given as Rs. 2,600. The Cost Price (CP) is Rs. 2,000. The profit is the difference between the selling price and the cost price:
\( \text{Profit}_2 = \text{SP}_2 - \text{CP} \)
Substitute the values:
\( \text{Profit}_2 = 2600 - 2000 \)
Calculating the value:
\( \text{Profit}_2 = 600 \)
So, the profit earned when selling the article for Rs. 2,600 is Rs. 600.
- Calculate the Gain Percentage (Profit Percentage) at the new price.
The gain percentage is calculated based on the Cost Price using the formula:
\( \text{Gain%} = \frac{\text{Profit}}{\text{CP}} \times 100 \)
Substitute the values of Profit<sub>2</sub> and CP:
\( \text{Gain%} = \frac{600}{2000} \times 100 \)
Simplify the expression:
\( \text{Gain%} = \frac{6}{20} \times 100 = \frac{3}{10} \times 100 \)
Calculating the final value:
\( \text{Gain%} = 30 \)
Thus, the gain percentage when the article is sold for Rs. 2,600 is 30%.
Summary of Calculations
| Item | Value |
|---|---|
| Selling Price 1 (SP<sub>1</sub>) | Rs. 2,200 |
| Profit % 1 (P%<sub>1</sub>) | 10% |
| Cost Price (CP) | Rs. 2,000 |
| Selling Price 2 (SP<sub>2</sub>) | Rs. 2,600 |
| Profit 2 (Profit<sub>2</sub>) | Rs. 600 |
| Gain % 2 (P%<sub>2</sub>) | 30% |
The gain percentage is 30%.
Revision Table: Profit and Loss Basics
| 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. | Profit = SP - CP |
| Loss | When SP < CP. | Loss = CP - SP |
| Profit Percentage (Gain %) | Profit expressed as a percentage of CP. | \( \text{Profit%} = \left(\frac{\text{Profit}}{\text{CP}}\right) \times 100 \) |
| Loss Percentage | Loss expressed as a percentage of CP. | \( \text{Loss%} = \left(\frac{\text{Loss}}{\text{CP}}\right) \times 100 \) |
Additional Information on Profit Calculation
Understanding the relationship between cost price, selling price, and profit percentage is fundamental in commercial arithmetic. The cost price is the base on which profit or loss is calculated. A profit means the selling price is higher than the cost price, while a loss means the selling price is lower than the cost price.
When the selling price and profit percentage are known, we can always work backwards to find the cost price using the formula \( \text{CP} = \frac{\text{SP}}{1 + \frac{\text{Profit%}}{100}} \). This derived formula is very useful in solving many profit and loss problems quickly. Similarly, if there was a loss percentage, the formula would be \( \text{CP} = \frac{\text{SP}}{1 - \frac{\text{Loss%}}{100}} \).
Once the cost price is established, calculating the new profit or loss and subsequently the percentage gain or loss for any new selling price becomes straightforward. It's simply a matter of comparing the new selling price to the constant cost price.
Important Questions from Profit and Loss
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?
If an article is sold for Rs. 355, there is a loss of 29%. At what price (in Rs.) should it be sold to gain 31% of profit?
