The cost price of an article is `7/6` times the selling price. What is the loss gain percentage (correct up to two decimal places)?

Options

A. Loss 14.29%
B. Gain 16.67%
C. Loss 16.67%
D. Gain 19.54%

Answer

To find the loss or gain percentage when the cost price (CP) of an article is \( \frac{7}{6} \) times the selling price (SP), we can follow these steps:

### Step 1: Define the relationship between CP and SP
Given that the cost price is \( \frac{7}{6} \) times the selling price, we can express this relationship mathematically:
\[ CP = \frac{7}{6} \times SP \]

### Step 2: Express CP in terms of SP
Let’s denote the selling price as \( SP = x \). Then, we can write:
\[ CP = \frac{7}{6} \times x \]

### Step 3: Calculate the loss
The loss incurred when selling the article can be calculated as:
\[ \text{Loss} = CP - SP \]
Substituting the values we have:
\[ \text{Loss} = \left(\frac{7}{6} \times x\right) - x \]
To simplify, we can express \( x \) as \( \frac{6}{6} \times x \):
\[ \text{Loss} = \frac{7}{6}x - \frac{6}{6}x = \frac{1}{6}x \]

### Step 4: Calculate the loss percentage
The loss percentage can be calculated using the formula:
\[ \text{Loss Percentage} = \left(\frac{\text{Loss}}{CP}\right) \times 100 \]
Substituting the values we have:
\[ \text{Loss Percentage} = \left(\frac{\frac{1}{6}x}{\frac{7}{6}x}\right) \times 100 \]
The \( x \) cancels out:
\[ \text{Loss Percentage} = \left(\frac{1}{7}\right) \times 100 \]
Calculating this gives:
\[ \text{Loss Percentage} = \frac{100}{7} \approx 14.2857\% \]

### Step 5: Round to two decimal places
Rounding \( 14.2857\% \) to two decimal places gives:
\[ \text{Loss Percentage} \approx 14.29\% \]

### Final Answer
The loss percentage is approximately **14.29%**.

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