Culture Compass

Location:HOME > Culture > content

Culture

Understanding Gain Percent in Cloth Sales

July 18, 2025Culture2504
Understanding Gain Percent in Cloth Sales In business and economics, u

Understanding Gain Percent in Cloth Sales

In business and economics, understanding the gain or profit percentage is crucial for determining the efficiency and profitability of a transaction. This article explains how to calculate the gain percent in a specific scenario involving the sale of cloth. We'll explore four different methods to solve this problem, each offering unique insights into the underlying mathematical principles.

Problem Statement

The problem we'll address is: "By selling 66 metres of cloth, a person gains the cost price of 22 metres. What is the gain percent?" This question requires understanding both cost price and selling price to find the gain percentage.

Method 1: Algebraic Approach

Step 1: Define Variables
Let the cost price (CP) of 1 metre of cloth be x.

Step 2: Express the Cost and Gain
The cost price of 66 metres of cloth is 66x.
Since the gain is equal to the cost price of 22 metres, the gain is 22x.

Step 3: Calculate the Selling Price (SP)
The selling price of 66 metres of cloth is SP CP of 66 metres Gain 66x 22x 88x.

Step 4: Calculate the Gain
Gain SP - CP 88x - 66x 22x.

Step 5: Calculate the Gain Percent
Gain Percent (Gain / CP) × 100 (22x / 66x) × 100 (22 / 66) × 100 (1 / 3) × 100 ≈ 33.33%.

Method 2: Direct Calculation

Step 1: Selling Price per Meter
If the selling price of 75 metres of cloth is Rs 75, then the selling price per metre is Rs 1.

Step 2: Cost Price Calculation
Since the gain is equal to the cost price of 15 metres, the cost price of 15 metres is Rs 75. Thus, the cost price per metre is Rs 5 (75/15 5).

Step 3: Cost Price of 75 Metres
The cost price of 75 metres is Rs 375 (5 × 75).

Step 4: Loss Calculation
The loss is Rs 300 (375 - 75).

Step 5: Loss Percent
Loss Percent (Loss / Cost Price) × 100 (300 / 375) × 100 80.

Method 3: Simplified Algebra

Step 1: Verify the Selling Price and Cost Price
Let the CP of each metre be x. So, CP of 66 m is 66x.
Gain 22x.
Gain Percentage (22x / 66x) × 100 33.33% when rounded to two decimal places.

Method 4: Ratio Approach

Step 1: Express the Relations Clearly
Selling price of 66 metres of cloth is equal to the cost price of 88 metres (CP of 66 metres CP of 22 metres SP of 66 metres).

Step 2: Calculate the Cost Price per Metre
CP of 1 m 66/88 3/4.

Step 3: Calculate the Selling Price per Metre
SP of 1 m 88/66 4/3.

Step 4: Calculate the Profit per Metre
Profit per metre SP of 1 m - CP of 1 m 4/3 - 3/4 7/12.

Step 5: Calculate the Profit Percent
Profit Percent (Profit / CP) × 100 (7/12 / 3/4) × 100 77.77% when reduced and rounded.

Conclusion

Understanding gain percent in sales problems involves a combination of algebra, direct calculation, and ratio approach. Each method offers a clear and unique way to solve such problems, contributing to a more comprehensive grasp of the subject. Whether solving business problems or academic exercises, knowledge of these techniques is invaluable.

Related Keywords

gain percent cost price selling price profit percentage