If a person sells 80% of the number of toys for an amount with which he purchased all the toys, then what is his profit percentage?

Options

A. 20
B. 22.5
C. 25
D. 40

Answer

To solve the problem, we need to determine the profit percentage based on the information given. Let's break it down step by step.

### Step 1: Define Variables
Let:
- \( C \) = Total cost price of all the toys
- \( N \) = Total number of toys
- \( S \) = Selling price of 80% of the toys

### Step 2: Calculate Selling Price
According to the problem, the person sells 80% of the toys for an amount equal to the total cost price of all the toys. Therefore:
- Selling price of 80% of the toys, \( S = C \)

### Step 3: Calculate Cost Price of Sold Toys
The number of toys sold is 80% of \( N \):
- Number of toys sold = \( 0.8N \)

The cost price of the toys sold (80% of the total toys) is:
- Cost price of 80% of the toys = \( 0.8 \times C \)

### Step 4: Determine Profit or Loss
Profit or loss is calculated as:
- Profit = Selling Price - Cost Price
- Profit = \( S - \text{Cost Price of 80% of toys} \)
- Profit = \( C - 0.8C = 0.2C \)

### Step 5: Calculate Profit Percentage
Profit percentage is calculated using the formula:
\[ \text{Profit Percentage} = \left( \frac{\text{Profit}}{\text{Cost Price}} \right) \times 100 \]
Substituting the values:
\[ \text{Profit Percentage} = \left( \frac{0.2C}{0.8C} \right) \times 100 \]
\[ \text{Profit Percentage} = \left( \frac{0.2}{0.8} \right) \times 100 = 25\% \]

### Final Answer
The profit percentage is **25%**.

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