Solving for Cost Price When Given Selling Price and Profit Percentage

Understanding the relationship between selling price, cost price, and profit percentage is crucial for any business or individual involved in the sale and purchase of goods. This article demonstrates a step-by-step method to calculate the cost price when provided with the selling price and a profit percentage. We will use the example of a book sold for Rs. 600 with a profit of 25% to elucidate the process.

Example Scenario

A book was sold at Rs. 600 with a profit of 25 percent. What is the cost price of the book?

Step-by-Step Solution

Let's solve this problem using multiple approaches to provide a comprehensive understanding.

Method 1: Direct Calculation

Given:

Selling Price (SP) Rs. 600 Profit 25% 0.25 (or 15/115 as a fraction)

The relationship between cost price (Cp) and selling price (SP) with profit can be expressed as:

SP Cp × (1 Profit %)

Substituting the given values:

600 Cp × (1.25)

Solving for Cp:

Cp 600 / 1.25 Rs. 480

Method 2: Using Percentage Formula

The formula to calculate cost price from selling price and profit percentage is:

Cp SP × 100 / (100 Profit %)

Substituting the given values:

Cp 600 × 100 / (100 25)

Cp 600 × 100 / 125

Cp 480

Method 3: Using Fractional Representation

The selling price is 125% of the cost price, so:

1.25Cp 600

Solving for Cp:

Cp 600 / 1.25 Rs. 480

Method 4: Using Algebraic Manipulation

Let the cost price be 'x'.

Given profit is 25%, so:

SP Cp (25/100) × Cp

600 x (25/100)x

600 x(1 0.25)

600 1.25x

Solving for x:

x 600 / 1.25 Rs. 480

Conclusion

From the multiple methods discussed, we can derive the same answer:

The cost price of the book is Rs. 480.

Understanding these calculations is essential for businesses and financial managers to make informed decisions and ensure profitability in any transaction.