Understanding the Relationship Between Cost Price, Selling Price, and Gross Profit in Mathematics

When dealing with sales and profit analysis, understanding the relationship between cost price, selling price, and gross profit is crucial. This article will explore how to calculate these values and understand their interplay. We will also provide a detailed solution to a specific mathematical problem.

Solving the Problem: Gross Profit and Selling Price Relationship

Consider a scenario where the gross profit is 34% of the selling price of an item. Additionally, x percentage of the selling price is equal to 25% of the cost price. This section aims to find the value of x using these given parameters.

Step-by-Step Solution

Step 1: Define Cost Price (C.P.) - We will assume the cost price of the item to be Rs 100. Step 2: Calculate Selling Price (S.P.) - Given that the gross profit is 34%, the selling price is calculated as 134% of the cost price. Therefore, S.P. 134 × 100/100 Rs 134. Step 3: Determine the Cost of 25% of the Cost Price - 25% of the cost price 25 × 100/100 Rs 25. Step 4: Set Up the Equation for x - The problem states that x percentage of the selling price is equal to 25% of the cost price. This can be written as:

x/100 × 134 25

Solving for x:

x 2500/134 18.66

Therefore, the value of x is 18.66.

Deriving Gross Profit from Selling Price and Cost Price

In sales and marketing, understanding the relationship between cost price and selling price is essential. Let's further elaborate on how to derive gross profit from these parameters.

Gross Profit Calculation

Gross Profit Calculation Formula - Gross Profit is given by Selling Price (S.P.) - Cost Price (C.P.). Example Calculation - Given the cost price (C.P.) as Rs 100 and selling price (S.P.) as Rs 134, the gross profit is calculated as:

134 - 100 34

Therefore, the gross profit is Rs 34, which is 34% of the selling price.

Conclusion

Understanding the relationships between cost price, selling price, and gross profit is vital for effective financial analysis and decision-making. By solving the specific problem provided, we have demonstrated a clear method to find the value of x and the gross profit percentage.

Additional Resources

For a deeper dive into related topics and further practice problems, refer to the following resources:

Cost Price and Selling Price Calculations Margin and Profit Ratios Finance and Accounting for Beginners

Keywords: gross profit, cost price, selling price, mathematics