Cost Price Calculation for Profit and Loss Scenarios in Business

Understanding the relationship between cost price and selling price is crucial in business and finance. In this article, we will explore how to calculate the cost price (CP) when there is both a loss and a profit associated with different selling prices (SP), and the loss is twice the profit. This concept is fundamental to financial analysis and is important for making informed business decisions.

Problem Statement and Methodology

Suppose a bag is sold at two different prices, Rs 1500 and Rs 2100. Selling the bag at Rs 1500 results in a loss, and selling it at Rs 2100 results in a profit. The condition given is that the loss is twice the profit. We are to find the cost price of the bag.

Solving the Equation

We will use algebra to solve the problem. Let the cost price CP of the bag be x.

1. **Loss when sold at Rs 1500**

Loss Cost Price - Selling Price

L x - 1500

2. **Profit when sold at Rs 2100**

Profit Selling Price - Cost Price

P 2100 - x

According to the problem, the loss is twice the profit:

L 2P

Solving for x:

L x - 1500
P 2100 - x
L 2P

x - 1500 2(2100 - x)

Expand the right side:

x - 1500 4200 - 2x

Rearrange the equation to bring all terms involving x to one side:

x 2x 4200 1500

3x 5700

Solve for x:

x 5700 / 3

x 1900

Thus, the cost price of the bag is Rs 1900.

Additional Examples

Here are some additional examples to understand the concept better:

Example 1: Selling Price and Loss Conditions

If the selling price at a profit is Rs 2200 and at a loss is Rs 1300, and the profit is twice the loss, the cost price can be calculated as follows:

S.P. at profit 2200 - CP P

S.P. at loss CP - 1300 L

P 2L

2200 - CP 2(CP - 1300)

Solve for CP:

2200 - CP 2CP - 2600

3CP 4800

CP 4800 / 3 1600

The cost price is Rs 1600.

Example 2: Direct Profit and Loss Relationship

In another situation, let the loss be x and the profit be 2x. If the cost price (CP) is 1300 and the selling price (SP) at a loss is 2200, then:

Profit is twice the loss

2200 - 1300 2(1300 - CP)

Solve for CP:

900 2(1300 - CP)

300 1300 - CP

CP 1300 - 300

CP 1600

The cost price is Rs 1600.

Conclusion

In conclusion, the cost price (CP) in a business scenario involving profit and loss is essential for successful financial analysis and decision-making. By understanding the relationship between SP and CP, we can accurately calculate the cost price. This knowledge is vital for business owners and financial analysts to make informed decisions and optimize their business operations.