If the selling price of 318 articles is equal to the cost price of 212 articles, then what is the loss percentage ?

Options

A. 20
B. 33 `1/3`
C. 40
D. 33 `2/3`

Answer

To solve the problem step by step, we will find the loss percentage based on the given information about the selling price (SP) and cost price (CP) of articles.

### Step 1: Understand the relationship between SP and CP
We are given that the selling price of 318 articles is equal to the cost price of 212 articles. This can be expressed as:
\[ SP_{318} = CP_{212} \]

### Step 2: Set up the equation
Let the cost price of one article be \( CP \) and the selling price of one article be \( SP \). Therefore, we can write:
\[ 318 \times SP = 212 \times CP \]

### Step 3: Find the ratio of SP to CP
From the equation above, we can derive the ratio of selling price to cost price:
\[ \frac{SP}{CP} = \frac{212}{318} \]

### Step 4: Simplify the ratio
Now, we simplify the fraction \( \frac{212}{318} \):
- Divide both the numerator and the denominator by their greatest common divisor (GCD), which is 106:
\[ \frac{SP}{CP} = \frac{2}{3} \]

### Step 5: Find the ratio of CP to SP
To find the ratio of cost price to selling price, we take the reciprocal of the previous ratio:
\[ \frac{CP}{SP} = \frac{3}{2} \]

### Step 6: Determine the loss
From the ratio \( \frac{CP}{SP} = \frac{3}{2} \), we can interpret this as:
- If the cost price (CP) is 3 units, then the selling price (SP) is 2 units.
- Therefore, the loss incurred is:
\[ \text{Loss} = CP - SP = 3 - 2 = 1 \text{ unit} \]

### Step 7: 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:
\[ \text{Loss Percentage} = \left( \frac{1}{3} \right) \times 100 = 33.33\% \]

### Final Answer
Thus, the loss percentage is \( 33 \frac{1}{3}\% \).

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