What is the cost price of an article when selling price is Rs. 2592 and the gain is 8%?
Rs. 2400
Calculating Cost Price from Selling Price and Gain
Understanding how to calculate the cost price (CP) when the selling price (SP) and the gain percentage are known is a fundamental concept in profit and loss problems. The relationship between these three elements is based on the gain or profit made on the sale of an article.
Relationship between Cost Price, Selling Price, and Gain
When there is a gain (profit) on selling an article, the selling price is greater than the cost price. The gain percentage is calculated on the cost price.
The formula connecting Selling Price (SP), Cost Price (CP), and Gain Percentage is:
\(\text{SP} = \text{CP} \times \left(1 + \frac{\text{Gain \%}}{100}\right)\)
In this problem, we are given the Selling Price (SP) and the Gain Percentage, and we need to find the Cost Price (CP). We can rearrange the formula to solve for CP:
\(\text{CP} = \frac{\text{SP}}{1 + \frac{\text{Gain \%}}{100}}\)
Step-by-Step Calculation
Let's apply the formula using the given values:
- Selling Price (SP) = Rs. 2592
- Gain Percentage = 8%
Now, substitute these values into the formula for CP:
\(\text{CP} = \frac{2592}{1 + \frac{8}{100}}\)
First, calculate the value in the denominator:
\(1 + \frac{8}{100} = 1 + 0.08 = 1.08\)
Now, divide the Selling Price by this value:
\(\text{CP} = \frac{2592}{1.08}\)
Performing the division:
\(\text{CP} = 2400\)
So, the cost price of the article is Rs. 2400.
Verification
Let's verify if selling an article costing Rs. 2400 with an 8% gain results in a selling price of Rs. 2592.
- Gain amount = 8% of CP = 8% of 2400
- Gain amount = \(\frac{8}{100} \times 2400 = 0.08 \times 2400 = 192\)
- Selling Price = Cost Price + Gain amount
- Selling Price = \(2400 + 192 = 2592\)
This matches the given selling price, confirming that our calculated cost price of Rs. 2400 is correct.
| Given Information | Value |
|---|---|
| Selling Price (SP) | Rs. 2592 |
| Gain Percentage | 8% |
Based on the calculation, the cost price is Rs. 2400.
Revision Table: Cost Price, Selling Price, and Profit
| Term | Definition | Formula (with Gain) | Formula (with Loss) |
|---|---|---|---|
| Cost Price (CP) | The price at which an article is purchased. | \( \text{CP} = \frac{\text{SP} \times 100}{100 + \text{Gain \%}} \) | \( \text{CP} = \frac{\text{SP} \times 100}{100 - \text{Loss \%}} \) |
| Selling Price (SP) | The price at which an article is sold. | \( \text{SP} = \text{CP} \times \left( \frac{100 + \text{Gain \%}}{100} \right) \) | \( \text{SP} = \text{CP} \times \left( \frac{100 - \text{Loss \%}}{100} \right) \) |
| Gain % | Profit expressed as a percentage of CP. | \( \text{Gain \%} = \frac{\text{Gain}}{\text{CP}} \times 100 \) | N/A |
| Loss % | Loss expressed as a percentage of CP. | N/A | \( \text{Loss \%} = \frac{\text{Loss}}{\text{CP}} \times 100 \) |
Additional Information on Profit and Loss Concepts
Profit and loss calculations are essential in business and everyday finance. Here are a few related concepts:
- Profit (Gain): When Selling Price > Cost Price. Profit = SP - CP.
- Loss: When Selling Price < Cost Price. Loss = CP - SP.
- Percentage Calculations: Gain% and Loss% are always calculated on the Cost Price, unless otherwise stated.
- Markup: The amount added to the cost price to determine the selling price.
- Discount: A reduction given on the marked price of an article.
Understanding these terms and formulas helps in solving various problems related to the pricing and sale of goods.
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