A trader sold some damaged garments for Rs. 7360 at a loss of 8%. Find the cost price of the garments.

Answer

To find the cost price of the garments sold by the trader, we can follow these steps:

### Step-by-Step Solution:

1. **Identify the Selling Price (SP) and Loss Percentage**:
- The selling price (SP) of the garments is given as Rs. 7360.
- The loss percentage is given as 8%.

2. **Understand the Relationship Between SP, CP, and Loss**:
- The formula for loss is given by:
\[ \text{Loss} = \text{Cost Price (CP)} - \text{Selling Price (SP)} \]
- The loss percentage can also be expressed as:
\[ \text{Loss Percentage} = \frac{\text{Loss}}{\text{CP}} \times 100 \]

3. **Express the Selling Price in Terms of Cost Price**:
- Since there is a loss of 8%, we can express the selling price in terms of the cost price (CP):
\[ SP = CP - \left(\frac{8}{100} \times CP\right) \]
- This simplifies to:
\[ SP = CP \left(1 - \frac{8}{100}\right) = CP \left(\frac{92}{100}\right) \]

4. **Substitute the Selling Price**:
- Now, substitute the selling price (SP) into the equation:
\[ 7360 = CP \left(\frac{92}{100}\right) \]

5. **Solve for Cost Price (CP)**:
- Rearranging the equation to find CP:
\[ CP = 7360 \times \frac{100}{92} \]
- Calculate the value:
\[ CP = 7360 \times \frac{100}{92} = 7360 \times 1.08695652 \approx 8000 \]

6. **Conclusion**:
- The cost price of the garments is Rs. 8000.