Question

If the total cost of 20 pairs of shoes is equal to the total revenue generated from the sale of 25 pairs of shoes, what is the percent of profit or loss made on the sale of each pair of shoes, assuming each pair of shoes cost the same dollar amount and each pair of shoes sold for the same dollar amount?

• A. 25% loss
• B. 25% profit
• C. 20% loss
• D. 20% profit
• E. 5% profit

Hint:

In profit/loss problems where the cost of X items equals the selling price of Y items, you can quickly determine if it's a profit or loss. If you sell more items (Y>X) to recoup the cost, it's a loss. If you sell fewer items (Y<X), it's a profit.

Answer 1

The Correct Option is C

Step 1: Understanding the Concept:
This problem deals with calculating profit or loss percentage. The key is to establish a relationship between the cost price (CP) and the selling price (SP) of a single item and then use the standard formula for profit/loss percentage.
Step 2: Key Formula or Approach:
Let \(C\) be the cost price of one pair of shoes.
Let \(S\) be the selling price (revenue) of one pair of shoes.
The formula for profit or loss percentage is:
\[ \text{Percentage} = \frac{S - C}{C} \times 100% \] A positive result indicates a profit, while a negative result indicates a loss.
Step 3: Detailed Explanation:
The problem states that the total cost of 20 pairs of shoes is equal to the total revenue from the sale of 25 pairs of shoes.
We can write this as an equation:
Total Cost of 20 pairs = Total Revenue of 25 pairs
\[ 20 \times C = 25 \times S \] To use the percentage formula, we need to find the relationship between S and C, specifically the ratio \( \frac{S}{C} \). We can rearrange the equation to find this ratio:
\[ \frac{S}{C} = \frac{20}{25} \] Simplify the fraction:
\[ \frac{S}{C} = \frac{4}{5} = 0.8 \] This ratio shows that the selling price is 0.8 times the cost price, meaning the shoes are sold for less than they cost. This indicates a loss.
Now, we can calculate the percentage loss:
\[ \text{Percentage} = \left( \frac{S}{C} - 1 \right) \times 100% \] \[ \text{Percentage} = (0.8 - 1) \times 100% \] \[ \text{Percentage} = -0.2 \times 100% = -20% \] The negative sign confirms that it is a loss.
Step 4: Final Answer:
The sale resulted in a 20% loss.