By selling an article for 360 there is a loss of 10%. What is the cost price (in Rs) of the article ?

Options

A. 324
B. 450
C. 400
D. 380

Answer

To find the cost price (CP) of the article given that it is sold for Rs. 360 with a loss of 10%, we can follow these steps:

### Step-by-Step Solution:

1. **Understand the relationship between Selling Price (SP), Cost Price (CP), and Loss**:
- We know that when there is a loss, the Selling Price is less than the Cost Price. The formula for loss percentage is:
\[ \text{Loss Percentage} = \frac{\text{Loss}}{\text{CP}} \times 100 \]

2. **Express Loss in terms of SP and CP**:
- The loss can be expressed as:
\[ \text{Loss} = \text{CP} - \text{SP} \]
- Substituting this into the loss percentage formula gives us:
\[ \text{Loss Percentage} = \frac{\text{CP} - \text{SP}}{\text{CP}} \times 100 \]

3. **Substituting the known values**:
- We know the Selling Price (SP) is Rs. 360 and the loss percentage is 10%. Therefore, we can set up the equation:
\[ 10 = \frac{\text{CP} - 360}{\text{CP}} \times 100 \]

4. **Simplifying the equation**:
- Dividing both sides by 10 gives:
\[ 1 = \frac{\text{CP} - 360}{\text{CP}} \times 10 \]
- Rearranging gives:
\[ 1 = \frac{10(\text{CP} - 360)}{\text{CP}} \]

5. **Cross-multiplying to eliminate the fraction**:
- This leads to:
\[ \text{CP} = 10(\text{CP} - 360) \]

6. **Distributing and rearranging**:
- Expanding the right side:
\[ \text{CP} = 10\text{CP} - 3600 \]
- Rearranging gives:
\[ 10\text{CP} - \text{CP} = 3600 \]
\[ 9\text{CP} = 3600 \]

7. **Solving for CP**:
- Dividing both sides by 9:
\[ \text{CP} = \frac{3600}{9} = 400 \]

### Final Answer:
The cost price (CP) of the article is Rs. 400.

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