Question
31. 20 pens were bought at \( \$ 2 \) each and sold at 2 for \( \$ 5 \). What is the percentage profit?
Ask by Edwards Spencer. in Guyana
Mar 14,2025
Upstudy AI Solution
Tutor-Verified Answer
Answer
The percentage profit is 25%.
Solution
**Step 1: Calculate the total cost**
The cost per pen is \( \$2 \). Since 20 pens were bought, the total cost is
\[
\text{Total Cost} = 20 \times 2 = \$40
\]
**Step 2: Calculate the selling price per pen**
The pens are sold at 2 for \( \$5 \). Thus, the selling price per pen is
\[
\text{Selling Price per Pen} = \frac{5}{2} = \$2.50
\]
**Step 3: Calculate the total revenue**
For 20 pens, the total revenue is
\[
\text{Total Revenue} = 20 \times 2.50 = \$50
\]
**Step 4: Calculate the profit**
The profit is the total revenue minus the total cost:
\[
\text{Profit} = 50 - 40 = \$10
\]
**Step 5: Calculate the percentage profit**
The percentage profit is given by the formula
\[
\text{Percentage Profit} = \left(\frac{\text{Profit}}{\text{Total Cost}}\right) \times 100
\]
Substitute the values:
\[
\text{Percentage Profit} = \left(\frac{10}{40}\right) \times 100 = 25\%
\]
Thus, the percentage profit is \( 25\% \).
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Simplify this solution Mind Expander
To find the percentage profit, we first need to determine the total cost and the total revenue. The cost of 20 pens at \( \$ 2 \) each is: \[ 20 \times 2 = \$ 40 \] When selling the pens at 2 for \( \$ 5 \), the revenue from selling all 20 pens (which is 10 pairs) is: \[ 10 \times 5 = \$ 50 \] Now, we can find the profit by subtracting the total cost from the total revenue: \[ \text{Profit} = \text{Revenue} - \text{Cost} = 50 - 40 = \$ 10 \] Finally, to find the percentage profit: \[ \text{Percentage Profit} = \left( \frac{\text{Profit}}{\text{Cost}} \right) \times 100 = \left( \frac{10}{40} \right) \times 100 = 25\% \] So, the percentage profit is \( 25\% \).
