The Profit and Loss in Cost Pricing: A Comprehensive Guide

Understanding the relationship between cost price, selling price, profit, and loss is fundamental in business and economics. This article provides a detailed explanation of how to calculate the cost price when given profit and loss relationships in a business scenario.

Introduction

When dealing with profit and loss, it is essential to understand how to set up and solve algebraic equations. This article will walk you through a specific example where the profit from a certain transaction is twice the loss from another transaction. By following the steps outlined, you can determine the cost price of an article accurately.

Step-by-Step Solution

Example Problem

Consider an article that can be sold for Rs. 744, resulting in a profit. However, if the same article is sold for Rs. 588, a loss is incurred. The profit from selling the article for Rs. 744 is twice the loss from selling it for Rs. 588. We need to determine the cost price (CP) of the article.

Solution

Let the cost price be denoted by Cp.

1. When the selling price (SP) is Rs. 744, the profit is:

SP1 - Cp 744 - Cp

Let the profit be represented by y. Therefore,
y 744 - Cp

2. When the selling price (SP) is Rs. 588, the loss is:

Cp - SP2 Cp - 588

Let the loss be represented by z. Therefore,
z Cp - 588

3. According to the problem, the profit is twice the loss:
2y z

Substitute y and z from the equations above:

2(744 - Cp) Cp - 588

Simplify the equation:

1488 - 2Cp Cp - 588

Add 2Cp to both sides:

1488 3Cp - 588

Add 588 to both sides:

2076 3Cp

Divide by 3:

Cp 692

Therefore, the cost price of the article is Rs. 692.

Alternative Approaches

There are different methods to solve the same problem. Here are a few alternative methods:

Method 1

- Let the cost price be x - SP1 - Cp y, where y is profit - Cp - SP2 z, where z is loss - 2y z - Solve the equations: - 12200 - x y - 2x - 1300 z - Solve for x, we get x 670

Method 2

- Let profit/loss X - 810 - X 530 - 2X 810 - 530 280 - X 140 - CP 810 - 140 Rs. 670

Method 3

- Let C.P. x, S.P. 2200, Profit S.P. - C.P. 2200 - x - New S.P. 1300, C.P. x, Loss x - 1300 - Given Profit 2 x Loss - 2200 - x 2x - 1300 - 2200 - x 2x - 2600 - x 2x 2600 2200 - 3x 4800 - x 4800 / 3 1600 - So, C.P. is Rs. 1600

Method 4

- Let the loss be x - Profit is 2x - Cost 1300 2x - 2200 - x 1300 2x - 2200 - x 1300 2x - 3x 900 - x 300 - Cost price Rs 1600

Method 5

- Let the cost price of the article be C - Given: Selling price at a profit is Rs. 2200, Selling price at a loss is Rs. 1300 - Profit is twice the loss: 2200 - C 2(C - 1300) - Solve for C: 2200 - C 2C - 2600 - 3C 4800 - C 1600 - Therefore, the cost price of the article is Rs. 1600

Conclusion

Understanding how to calculate cost prices based on profit and loss relationships is crucial for effective business operations. By following the outlined steps, you can accurately determine the cost price of an article, which is essential for making informed business decisions.