Solving Profit and Cost Price Problems: A Comprehensive Guide for SEO

Seoers often need to demonstrate the application of mathematical concepts to solve real-world business problems. This article offers a detailed explanation of a specific problem involving tables and chairs, where we calculate the cost and profit based on given data. The step-by-step approach will help SEO professionals and beginners to understand the process and apply similar methodologies to their work.

Introduction to the Problem

A businessman purchases 5 tables and 9 chairs for a total of Rs. 15400. He sells the tables at a 10% profit and the chairs at a 20% profit. Given that his total profit from selling these items is Rs. 2080, the task is to calculate the cost price of 3 chairs.

Defining Cost Prices of Tables and Chairs

Let us denote the cost price of one table as C_t and the cost price of one chair as C_c. We can establish the first equation based on the total cost of purchase:

5C_t 9C_c 15400 (1)

Selling Prices Calculation

The selling prices for one table and one chair, considering the profit margins, are calculated as follows:

Selling Price of one table (SP_t) C_t 0.1C_t 1.1C_t Selling Price of one chair (SP_c) C_c 0.2C_c 1.2C_c

Thus, the total selling price for 5 tables and 9 chairs is:

5(1.1C_t) 9(1.2C_c) 5.5C_t 10.8C_c (2)

Total Profit Calculation

The total profit equation is:

5.5C_t 10.8C_c 5C_t 9C_c 2080

Using equation (1), we can substitute and simplify this to:

5.5C_t 10.8C_c 17480 (3)

Solving the Equations

To solve for C_c, we multiply equation (1) by 1.1 to align the coefficients of C_t:

5.5C_t 9.9C_c 16940 (4)

By subtracting equation (4) from equation (3), we isolate the cost price of a chair:

0.9C_c 540

C_c 540 / 0.9 600

Thus, the cost price of one chair is Rs. 600. For three chairs, the cost is:

3C_c 3 × 600 1800

Therefore, the cost price of 3 chairs is Rs. 1800.

Alternative Solutions

A simpler solution involves directly setting the CP of a table as T and a chair as C:

5T 9C 15400 5.5T 10.8C 17480 Solving these, we find C 600 Therefore, 3C 1800

And for the direct algebraic method:

5C_t 9C_c 15400 0.5C_t 1.8C_c 2080 9C_c 5400 C_c 600 Therefore, 3C_c 1800

Conclusion

This problem demonstrates the application of algebraic equations to solve real-life business and marketing scenarios. SEOers can use these techniques to optimize content, product pricing, and profit margins, ensuring their business strategies are data-driven and effective. Understanding the concepts of cost price and profit is crucial for any business analysis, and this article provides a solid foundation.