Solving Cost Price Problems Using Selling Prices and Profit/Loss Percentages

Understanding how to calculate the cost price of items based on their selling prices and profit or loss percentages is a fundamental concept in business and economics. In this article, we will explore a problem involving two articles, each sold at different profit and loss percentages with the same selling price.

Let's delve into the problem:

Problem Statement

Two articles are bought for Rupees 1400. One of them is sold at a 20% profit, and the other at a 10% loss. If the selling prices of both articles are the same, find the cost price of each article.

Solution

Let the cost price of the first article be x Rupees. Consequently, the cost price of the second article is 1400 - x Rupees.

Selling Price (SP) Calculation

The first article is sold at a 20% profit:

SP1 x 0.2x 1.2x

The second article is sold at a 10% loss:

SP2 (1400 - x) - 0.1(1400 - x) 0.9(1400 - x)

Since the selling prices are the same:

1.2x 0.9(1400 - x)

Solving for x

Let's solve the equation to find the value of x.

First, let's expand the right side of the equation:

1.2x 0.9(1400 - x) 1260 - 0.9x

Next, combine like terms:

1.2x 0.9x 1260

2.1x 1260

Divide both sides by 2.1:

x 1260 / 2.1 600

Calculating Cost Prices

The cost price of the first article is Rs. 600.

The cost price of the second article is:

1400 - 600 Rs. 800

Verification

To verify the solution, let's calculate the selling prices:

SP of the first article: 1.2 × 600 Rs. 720

SP of the second article: 0.9 × (1400 - 600) 0.9 × 800 Rs. 720

Both selling prices match, confirming our solution.

Conclusion

Therefore, the cost price of the first article is Rs. 600, and the cost price of the second article is Rs. 800.

Additional Examples for Practice

Practice is key to mastering these types of problems. Here are a few additional examples for you to solve:

Two items are bought for Rs. 1600. One is sold at a 15% profit, and the other at a 5% loss. If their selling prices are the same, what is the cost price of each item? A retailer buys two articles for Rs. 2000. One is sold at 30% profit, and the other at 10% loss. If their selling prices are equal, find their cost prices.

For further guidance, consider using online resources or seeking assistance from a math tutor.

Key Points to Remember

The cost price (CP) is the original price of an item before any profit or loss is applied. The selling price (SP) is calculated by adding the profit percentage to the cost price or subtracting the loss percentage from the cost price. When the SP of two items is the same with different profit and loss percentages, use the equations to find the CP.