A man buys apples at a certain price per dozen and sells them at eight times that price per hundred. His gain or loss per cent is ________.

Options

A. a. 4%
B. b. `-4%`
C. c. `5%`
D. d. `-5%`

Answer

To solve the problem step by step, we will first define the variables and then calculate the cost price, selling price, and the percentage of gain or loss.

### Step 1: Define the Cost Price
Let's assume the cost price (CP) of 12 apples (1 dozen) is ₹12.

### Step 2: Calculate the Cost Price per Apple
Since there are 12 apples in a dozen, the cost price per apple (CP per apple) can be calculated as follows:
\[ \text{CP per apple} = \frac{\text{CP for 12 apples}}{12} = \frac{12}{12} = ₹1 \]

### Step 3: Define the Selling Price
The problem states that he sells the apples at 8 times the cost price per 100 apples. Therefore, we first calculate the selling price (SP) for 100 apples:
\[ \text{SP for 100 apples} = 8 \times \text{CP for 12 apples} = 8 \times 12 = ₹96 \]

### Step 4: Calculate the Selling Price per Apple
Now, we can find the selling price per apple (SP per apple):
\[ \text{SP per apple} = \frac{\text{SP for 100 apples}}{100} = \frac{96}{100} = ₹0.96 \]

### Step 5: Calculate the Loss
Now, we can find the loss incurred per apple:
\[ \text{Loss per apple} = \text{CP per apple} - \text{SP per apple} = 1 - 0.96 = ₹0.04 \]

### Step 6: Calculate the Loss Percentage
To find the loss percentage, we use the formula:
\[ \text{Loss Percentage} = \left(\frac{\text{Loss}}{\text{CP}} \times 100\right) \]
Substituting the values:
\[ \text{Loss Percentage} = \left(\frac{0.04}{1} \times 100\right) = 4\% \]

### Final Answer
The loss percentage is **4%**.

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