If the cost price of 10 shirts is equal to the selling price of 8 shirts, then which of the following is true for the transaction?

Options

A. Profit of 25%
B. Loss of 25%
C. Profit of 20%
D. Loss of 20%

Answer

To solve the problem step by step, we will analyze the given information and calculate the profit percentage based on the cost price (CP) and selling price (SP) of the shirts.

### Step 1: Understand the relationship between CP and SP
According to the problem, the cost price of 10 shirts is equal to the selling price of 8 shirts. We can express this mathematically as:
\[ 10 \times \text{CP} = 8 \times \text{SP} \]

### Step 2: Express CP in terms of SP
From the equation above, we can isolate CP:
\[ \text{CP} = \frac{8}{10} \times \text{SP} \]
This simplifies to:
\[ \text{CP} = \frac{4}{5} \times \text{SP} \]

### Step 3: Find the ratio of CP to SP
From the expression we derived, we can see that:
\[ \text{CP} : \text{SP} = 4 : 5 \]
This indicates that the cost price is less than the selling price, which suggests a profit.

### Step 4: Calculate the profit
To find the profit, we use the formula:
\[ \text{Profit} = \text{SP} - \text{CP} \]
Substituting the value of CP:
\[ \text{Profit} = \text{SP} - \frac{4}{5} \text{SP} \]
This simplifies to:
\[ \text{Profit} = \frac{1}{5} \text{SP} \]

### Step 5: Calculate the profit percentage
The profit percentage can be calculated using the formula:
\[ \text{Profit Percentage} = \left( \frac{\text{Profit}}{\text{CP}} \right) \times 100 \]
Substituting the values:
\[ \text{Profit Percentage} = \left( \frac{\frac{1}{5} \text{SP}}{\frac{4}{5} \text{SP}} \right) \times 100 \]
The SP cancels out:
\[ \text{Profit Percentage} = \left( \frac{1}{4} \right) \times 100 \]
This simplifies to:
\[ \text{Profit Percentage} = 25\% \]

### Conclusion
The transaction results in a profit of 25%.

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