If the cost price of 12 items is equal to the selling price of 16 items, the loss percent is

Options

A. 0.2
B. 0.25
C. 0.3
D. 0.35

Answer

To solve the problem step by step, we will use the information given in the question.

### Step 1: Understand the relationship between Cost Price (CP) and Selling Price (SP)
We know that the cost price of 12 items is equal to the selling price of 16 items. This can be expressed mathematically as:
\[ 12 \times \text{CP} = 16 \times \text{SP} \]

### Step 2: Express CP in terms of SP
From the equation above, we can rearrange it to find the ratio of CP to SP:
\[ \frac{\text{CP}}{\text{SP}} = \frac{16}{12} \]
This simplifies to:
\[ \frac{\text{CP}}{\text{SP}} = \frac{4}{3} \]

### Step 3: Determine the loss
Since the cost price (CP) is greater than the selling price (SP), we can express the loss as:
\[ \text{Loss} = \text{CP} - \text{SP} \]
To find the loss percentage, we need to express loss in terms of CP:
\[ \text{Loss} = \text{CP} - \text{SP} = \text{CP} - \frac{3}{4} \text{CP} = \frac{1}{4} \text{CP} \]

### Step 4: Calculate the loss percentage
The loss percentage can be calculated using the formula:
\[ \text{Loss Percentage} = \left( \frac{\text{Loss}}{\text{CP}} \right) \times 100 \]
Substituting the loss we found:
\[ \text{Loss Percentage} = \left( \frac{\frac{1}{4} \text{CP}}{\text{CP}} \right) \times 100 = \frac{1}{4} \times 100 = 25\% \]

### Conclusion
The loss percentage is 25%.