The selling price of an article is `1(1)/(12)` of the cost price. What is the profit percentage?

Options

A. 8
B. `8(1)/(3)`
C. `8(1)/(2)`
D. `8(1)/(6)`

Answer

To solve the problem step by step, we will first express the selling price in terms of the cost price and then calculate the profit percentage.

### Step 1: Understand the relationship between selling price and cost price
The problem states that the selling price (SP) of an article is \(1 \frac{1}{12}\) times the cost price (CP).

### Step 2: Convert the mixed fraction to an improper fraction
The mixed fraction \(1 \frac{1}{12}\) can be converted to an improper fraction:
\[ 1 \frac{1}{12} = \frac{12 + 1}{12} = \frac{13}{12} \]
Thus, we have:
\[ SP = \frac{13}{12} \times CP \]

### Step 3: Express the profit in terms of cost price
Profit (P) is defined as the difference between selling price and cost price:
\[ P = SP - CP \]
Substituting the expression for SP:
\[ P = \left(\frac{13}{12} \times CP\right) - CP \]
To combine the terms, we express CP as \(\frac{12}{12} \times CP\):
\[ P = \frac{13}{12} \times CP - \frac{12}{12} \times CP = \frac{1}{12} \times CP \]

### Step 4: Calculate the profit percentage
Profit percentage is calculated using the formula:
\[ \text{Profit Percentage} = \left(\frac{P}{CP}\right) \times 100 \]
Substituting the expression for P:
\[ \text{Profit Percentage} = \left(\frac{\frac{1}{12} \times CP}{CP}\right) \times 100 \]
The CP cancels out:
\[ \text{Profit Percentage} = \left(\frac{1}{12}\right) \times 100 \]
Calculating this gives:
\[ \text{Profit Percentage} = \frac{100}{12} = 8.33\% \]

### Final Answer
The profit percentage is \(8 \frac{1}{3}\%\).

---