Find the cost price of an article which is sold for Rs. 220 at a loss of 12%.

Answer

To find the cost price (CP) of an article sold for Rs. 220 at a loss of 12%, we can follow these steps:

### Step-by-Step Solution:

1. **Identify the given values**:
- Selling Price (SP) = Rs. 220
- Loss Percentage = 12%

2. **Understand the relationship between CP, SP, and Loss**:
- The formula for loss percentage is given by:
\[ \text{Loss Percentage} = \frac{\text{CP} - \text{SP}}{\text{CP}} \times 100 \]

3. **Substitute the known values into the formula**:
- We know that the loss percentage is 12%, so we can set up the equation:
\[ 12 = \frac{\text{CP} - 220}{\text{CP}} \times 100 \]

4. **Convert the percentage to a fraction**:
- Dividing both sides by 100 gives:
\[ \frac{12}{100} = \frac{\text{CP} - 220}{\text{CP}} \]
- Simplifying \(\frac{12}{100}\) gives \(\frac{3}{25}\):
\[ \frac{3}{25} = \frac{\text{CP} - 220}{\text{CP}} \]

5. **Cross-multiply to eliminate the fraction**:
- This leads to:
\[ 3 \times \text{CP} = 25 \times (\text{CP} - 220) \]

6. **Expand and rearrange the equation**:
- Expanding the right side:
\[ 3 \times \text{CP} = 25 \times \text{CP} - 5500 \]
- Rearranging gives:
\[ 5500 = 25 \times \text{CP} - 3 \times \text{CP} \]
\[ 5500 = 22 \times \text{CP} \]

7. **Solve for CP**:
- Dividing both sides by 22:
\[ \text{CP} = \frac{5500}{22} \]
- Simplifying gives:
\[ \text{CP} = 250 \]

### Final Answer:
The cost price of the article is Rs. 250.

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