Question

Question:Distinguish between gross profit as a percentage of cost and gross profit as a percentage of sales price. Convert the following gross profit percentages based on cost togross profit percentages based on sales price: 25% and 331 /3%. Convert the following gross profit percentages based on sales price to gross profit percentages based on cost: 331 /3% and 60%.

Short answer

Gross profit as a percentage of the cost indicates the gross profit percentage on the basis of cost price, whereas gross profit as a percentage of the sales price indicates the gross profit percentage on the basis of the selling price.

Gross profit based on sales price equals 20% and 24.99%, respectively. Gross profit based on cost equals 49.99% and 150%.

Step-by-step solution

Step 1: 

Gross profit on selling price is determined by dividing percentage markup on the cost by the sum of 100% and percentage markup on cost, whereas gross profit on cost is determined by dividing gross profit on selling price by the difference of 100% and gross profit on selling price.

Step2:

Gross on selling price for gross profit on the cost of 25% is calculated as follows:

$$\begin{gathered} \mathbf{GrossProfitonSellingPrice}\mathbf{=}\frac{\mathbf{PercentageMarkuponCost}}{\mathbf{100}\mathbf{\%}\mathbf{+}\mathbf{PercentageMarkuponCost} \\ \mathbf{=}\frac{\mathbf{25}\mathbf{\%}}{\mathbf{100}\mathbf{\%}\mathbf{+}\mathbf{25}\mathbf{\%}} \\ \mathbf{=}\mathbf{20}\mathbf{\%}} \end{gathered}$$

Step 3:

Gross on selling price for gross profit on the cost of 33 1/3% is calculated as follows:

$$\begin{gathered} \mathbf{GrossProfitonSellingPrice}\mathbf{=}\frac{\mathbf{PercentageMarkuponCost}}{\mathbf{100}\mathbf{\%}\mathbf{+}\mathbf{PercentageMarkuponCost} \\ \mathbf{=}\frac{\mathbf{33}{\displaystyle \frac{\mathbf{1}}{\mathbf{3}}}\mathbf{\%}}{\mathbf{100}\mathbf{\%}\mathbf{+}\mathbf{33}\frac{\mathbf{1}}{\mathbf{3}}\mathbf{\%}} \\ \mathbf{=}\mathbf{24}\mathbf{.}\mathbf{99}\mathbf{\%}} \end{gathered}$$

Step 4:

Gross on cost for gross profit on the selling price of 33 1/3% is calculated as follows:

$$\begin{gathered} \mathbf{GrossProfitonCost}\mathbf{=}\frac{\mathbf{GrossProfitonSellingPrice}}{\mathbf{100}\mathbf{\%}\mathbf{-}\mathbf{GrossProfitonSellingPrice} \\ \mathbf{=}\frac{\mathbf{33}\frac{\mathbf{1}}{\mathbf{3}}\mathbf{\%}}{\mathbf{100}\mathbf{\%}\mathbf{-}\mathbf{33}\frac{\mathbf{1}}{\mathbf{3}}\mathbf{\%}} \\ \mathbf{=}\mathbf{49}\mathbf{.}\mathbf{99}\mathbf{\%}} \end{gathered}$$

Step 5:

Gross on cost for gross profit on the selling price of 60% is calculated as follows:

$$\begin{gathered} \mathbf{GrossProfitonCost}\mathbf{=}\frac{\mathbf{GrossProfitonSellingPrice}}{\mathbf{100}\mathbf{\%}\mathbf{-}\mathbf{GrossProfitonSellingPrice} \\ \mathbf{=}\frac{\mathbf{60}\mathbf{\%}}{\mathbf{100}\mathbf{\%}\mathbf{-}\mathbf{60}\mathbf{\%}} \\ \mathbf{=}\mathbf{150}\mathbf{\%}} \end{gathered}$$