Profit and Loss in Selling Items: A Mathematical Insight

Solving profit and loss problems not only enhances mathematical skills but also helps in understanding real-world scenarios. In this article, we explore a problem where a seller incurs a loss and the subsequent actions needed to achieve a desired profit. This analysis is crucial for anyone looking to increase their understanding of financial management and businesses.

Problem Statement

A seller sells 12 items for 1 rupee and incurs a 20% loss. The challenge is to determine the number of items he needs to sell for 1 rupee to achieve a 20% profit.

Understanding the Problem

The first step in solving the problem is to understand the relationship between cost price (CP), selling price (SP), and profit or loss. The formula for loss is as follows:

Loss CP - SP

Step 1: Calculate the Cost Price (CP)

Given that the SP of 12 items is 1 rupee and the loss is 20%, we can use the following formula to find the CP:

SP CP × (1 - Loss)

Plugging in the given values:

1 CP × (1 - 0.20) CP × 0.80

Solving for CP:

CP 1 / 0.80 1.25 rupees for 12 items

Now, to find the CP of one item:

CP of one item 1.25 / 12 ≈ 0.1042 rupees

Step 2: Calculate the Selling Price (SP) for a 20% Gain

To achieve a 20% profit, we use the formula for gain:

SP CP × (1 Gain)

Plugging in the CP of one item:

SP of one item 0.1042 × 1.20 ≈ 0.1250 rupees

Step 3: Determine the Number of Items to Sell for 1 Rupee

To find out how many items he should sell for 1 rupee at this new SP:

Number of items 1 / SP of one item 1 / 0.1250 8

Conclusion

To gain a 20% profit, the seller should sell 8 items for 1 rupee. This problem demonstrates the relationship between cost price, selling price, and profit, which are essential concepts in business mathematics.

Understanding these principles can help in making informed decisions in financial management and ensure profitability in any business venture.

Related Keywords

cost price, selling price, profit calculation