After selling 63 article a man losses SP of 9 article find his loss% ?

Options

A. `16 (2)/(3)%`
B. `14(2)/(3)%`
C. `20%`
D. `12.5%`

Answer

To find the loss percentage when a man sells 63 articles and incurs a loss equivalent to the selling price of 9 articles, we can follow these steps:

### Step 1: Define the Selling Price per Article
Let the selling price (SP) of each article be \( x \) rupees.

### Step 2: Calculate Total Selling Price for 63 Articles
The total selling price (SP) for 63 articles is:
\[ \text{Total SP} = 63 \times x = 63x \]

### Step 3: Calculate the Loss
According to the problem, the man loses the selling price of 9 articles. Therefore, the loss is:
\[ \text{Loss} = 9 \times x = 9x \]

### Step 4: Determine the Cost Price (CP)
To find the cost price (CP), we need to understand that the loss incurred is the difference between the cost price and the selling price. Therefore, we can express it as:
\[ \text{CP} - \text{Total SP} = \text{Loss} \]
Substituting the known values:
\[ \text{CP} - 63x = 9x \]

### Step 5: Solve for Cost Price (CP)
Rearranging the equation gives:
\[ \text{CP} = 63x + 9x = 72x \]

### Step 6: Calculate the Loss Percentage
Loss percentage is calculated using the formula:
\[ \text{Loss \%} = \left( \frac{\text{Loss}}{\text{CP}} \right) \times 100 \]
Substituting the values we have:
\[ \text{Loss \%} = \left( \frac{9x}{72x} \right) \times 100 \]

### Step 7: Simplify the Loss Percentage
The \( x \) cancels out:
\[ \text{Loss \%} = \left( \frac{9}{72} \right) \times 100 = \left( \frac{1}{8} \right) \times 100 = 12.5\% \]

### Final Answer
The loss percentage is \( 12.5\% \).

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