Calculating Profit Percentage from Selling Price: A Practical Example

A common question in financial mathematics involves determining the profit percentage when given the relationship between the selling price and the profit. Let's explore a practical example that illustrates how to solve such a problem.

Problem Statement:

On the selling of a fan, the profit is two sevenths of its selling price. Determine the profit percentage.

Step-by-Step Solution:

Step 1: Define Variables

Selling Price (SP): Let the selling price of the fan be denoted by SP. Profit: Given that the profit is two sevenths of the selling price, we can express the profit as Profit 2/7 SP.

Step 2: Calculate Cost Price (CP)

Profit is defined as:

Profit SP - CP

From this, we can rearrange the equation to find the cost price:

CP SP - Profit SP - (2/7)SP (5/7)SP

Step 3: Calculate Profit Percentage

The profit percentage is calculated using the formula:

Profit Percentage (Profit / CP) * 100

Substituting the values we found:

Profit Percentage (2/7 SP) / ((5/7) SP) * 100

The SP in the numerator and denominator cancel out:

Profit Percentage (2/5) * 100 40%

Conclusion:

Therefore, the profit percentage when the profit is two sevenths of the selling price is 40%.

Verification:

Let's verify the solution with numerical values:

Assume the selling price (SP) is 100:

Profit (2/7) * 100 200/7 Cost Price (CP) SP - Profit 100 - 200/7 500/7 Profit Percentage (Profit / CP) * 100 (200/7) / (500/7) * 100 40%

This confirms our earlier calculations.

Additional Insights:

It's important to note that the profit percentage can be calculated differently depending on the basis (i.e., whether the profit is based on the selling price or the cost price). However, the question specifically asked for the profit percentage based on the selling price, which results in 40% as shown above.

Frequently Asked Questions:

Question 1: What is profit percentage?

Answer: Profit percentage is a financial metric that represents the ratio of profit earned to the cost price, multiplied by 100. It is often expressed as a percentage and is a key indicator of profitability.

Question 2: How do you calculate the profit percentage?

Answer: The profit percentage is calculated using the formula:

Profit Percentage (Profit / Cost Price) * 100

Where Profit is the difference between the selling price and the cost price.

Question 3: How does the selling price affect the profit percentage?

Answer: The selling price directly impacts the profit percentage. When the selling price is increased while the cost remains constant, the profit percentage will increase. Conversely, lowering the selling price will decrease the profit percentage.