Calculating the Cost Price of a Product with a Given Profit Percentage
Understanding the concept of cost price and selling price is crucial for businesses and individual sellers alike. When a product is sold with a profit margin of 20%, and the selling price is Rs. 540, how can we determine the cost price? This article will guide you through various methods to solve this problem, ensuring clarity and ease in comprehension. Whether you are a student, a business owner, or a professional in the field, knowing these calculations can save you valuable time and resources.
Method 1: Algebraic Approach Using the Cost Price as the Variable
Let the cost price be denoted as ( X ). If the profit is 20%, we can express the profit as:
Profit ( frac{20}{100} times X frac{X}{5} )
The selling price is the sum of the cost price and the profit:
Selling Price ( X frac{X}{5} frac{6X}{5} )
Given that the selling price is Rs. 540:
( frac{6X}{5} 540 )
Solving for ( X ):
( X 540 times frac{5}{6} 450 )
Therefore, the cost price of the product is Rs. 450.
Method 2: Direct Calculation Using Selling Price and Profit Percentage
In this method, we directly calculate the cost price using the formula:
Cost Price Selling Price / (1 Profit Percentage)
Given:
Selling Price (SP) Rs. 540
Profit Percentage 20%
Substitute the values into the formula:
Cost Price (CP) ( frac{540}{1 frac{20}{100}} frac{540}{1.20} 450 )
Therefore, the cost price of the product is Rs. 450.
Method 3: Simplified Calculation Using a Ratio
An alternative and more streamlined approach is to use a ratio based on the profit percentage. If the profit is 20%, then:
120% of the cost price is equivalent to the selling price:
120% of cost price 540
Thus, 100% of the cost price can be calculated as:
Cost Price ( frac{540 times 100}{120} 450 )
Therefore, the cost price of the product is Rs. 450.
Conclusion
Understanding the relationship between selling price and cost price with a given profit percentage is essential for any business or individual. By using the algebraic approach, direct calculation methods, or simplified ratios, you can accurately determine the cost price of a product. Remember, the key steps include identifying the given selling price, profit percentage, and then applying the appropriate formula to find the cost price.
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