A man buys some articles at P per dozen and sells them at `(P)/(8)` per piece. His profit per cent is

Options

A. 0.3
B. 0.4
C. 0.5
D. 0.6

Answer

To solve the problem, we will follow these steps:

### Step 1: Determine the Cost Price (CP) of one dozen articles.
The man buys articles at P rupees per dozen. Therefore, the cost price (CP) for one dozen articles is:
\[ \text{CP} = P \]

**Hint:** Remember that the cost price given is for a dozen articles, so you don't need to divide by 12.

### Step 2: Determine the Selling Price (SP) of one piece.
The selling price (SP) of one piece is given as \( \frac{P}{8} \).

**Hint:** This is the price for a single article, so keep it as is for now.

### Step 3: Calculate the Selling Price (SP) of one dozen articles.
Since there are 12 pieces in a dozen, we can find the selling price for one dozen articles by multiplying the selling price of one piece by 12:
\[ \text{SP for one dozen} = 12 \times \left(\frac{P}{8}\right) = \frac{12P}{8} = \frac{3P}{2} \]

**Hint:** When multiplying, make sure to simplify the fraction to get the selling price for a dozen.

### Step 4: Calculate the Profit.
Profit is calculated as the difference between the selling price and the cost price:
\[ \text{Profit} = \text{SP} - \text{CP} = \frac{3P}{2} - P \]
To subtract, convert P into a fraction:
\[ P = \frac{2P}{2} \]
Now, substituting:
\[ \text{Profit} = \frac{3P}{2} - \frac{2P}{2} = \frac{1P}{2} = \frac{P}{2} \]

**Hint:** Make sure to have a common denominator when subtracting fractions.

### Step 5: Calculate the Profit Percentage.
Profit percentage is calculated using the formula:
\[ \text{Profit Percentage} = \left(\frac{\text{Profit}}{\text{CP}}\right) \times 100 \]
Substituting the values we have:
\[ \text{Profit Percentage} = \left(\frac{\frac{P}{2}}{P}\right) \times 100 = \left(\frac{1}{2}\right) \times 100 = 50\% \]

**Hint:** Remember to multiply by 100 to convert the fraction into a percentage.

### Final Answer:
The profit percentage is **50%**.

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