Calculating Percentage Benefit on Selling Price with a 20% Profit on Purchase Price

In a scenario where you have a 20% profit on the purchase price, you might wonder what this translates to in terms of the benefit on the selling price. Let's explore this step-by-step to understand it better.

Understanding the Concept

Let's denote the purchase price as P.

Calculating the Selling Price

When there is a 20% profit on the purchase price, the profit can be calculated as:

Profit 0.20 times P

Consequently, the selling price (SP) can be found by adding this profit to the purchase price:

SP P 0.20P 1.20P

Calculating the Percentage Benefit on the Selling Price

Now, let's determine the percentage benefit on the selling price. The benefit here refers to the profit, which is:

Profit 0.20P

The percentage benefit on the selling price is calculated as:

Percentage Benefit left( frac{Profit}{SP} right) times 100 left( frac{0.20P}{1.20P} right) times 100 approx 16.67%

Therefore, the percentage benefit on the selling price when there is a 20% profit on the purchase price is approximately 16.67%.

Alternative Algebraic Approach

Another way to approach this problem is through an algebraic solution. Here is a detailed explanation:

Let's denote the selling price as S and the cost price as C.

Based on the selling price, the profit can be expressed as:

P 0.20S

By substituting the value of P in the equation for the selling price, we get:

S C 0.20S

Rearranging the equation:

C 0.80S

Now, we need to find what is the percentage of profit over the cost price:

frac{P}{C} frac{0.20S}{0.80S} frac{0.20}{0.80} frac{2}{8} 0.25 25%

The Algebraic approach also highlights the beauty of this method in eliminating variables to find the desired percentage.

Conclusion

Understanding the relationship between profit, purchase price, and selling price can be crucial for effective financial management in various industries. Whether you prefer the straightforward calculation or the algebraic approach, both methods lead to the same conclusion: a 20% profit on the purchase price results in approximately a 16.67% benefit on the selling price.