What will be the cost price of an item if it is sold for Rs 187 after a loss of `15%`?

Answer

To find the cost price of an item sold for Rs. 187 after a loss of 15%, we can follow these steps:

### Step-by-Step Solution:

1. **Understand the given values**:
- Selling Price (SP) = Rs. 187
- Loss Percentage = 15%

2. **Set up the formula for loss**:
- The formula for loss is given by:
\[ \text{Loss} = \text{Cost Price (CP)} - \text{Selling Price (SP)} \]

3. **Express loss in terms of cost price**:
- We know that the loss percentage is given by:
\[ \text{Loss Percentage} = \frac{\text{Loss}}{\text{Cost Price}} \times 100 \]
- Rearranging this formula gives us:
\[ \text{Loss} = \frac{\text{Loss Percentage} \times \text{Cost Price}}{100} \]
- Substituting the known loss percentage:
\[ \text{Loss} = \frac{15 \times \text{CP}}{100} \]

4. **Substitute the loss into the loss formula**:
- Now we can substitute this expression for loss back into the loss formula:
\[ \text{CP} - \text{SP} = \frac{15 \times \text{CP}}{100} \]
- Plugging in the selling price:
\[ \text{CP} - 187 = \frac{15 \times \text{CP}}{100} \]

5. **Clear the fraction**:
- To eliminate the fraction, multiply the entire equation by 100:
\[ 100 \times \text{CP} - 18700 = 15 \times \text{CP} \]

6. **Rearrange the equation**:
- Now, bring all terms involving CP to one side:
\[ 100 \times \text{CP} - 15 \times \text{CP} = 18700 \]
- This simplifies to:
\[ 85 \times \text{CP} = 18700 \]

7. **Solve for CP**:
- Divide both sides by 85:
\[ \text{CP} = \frac{18700}{85} \]
- Calculating this gives:
\[ \text{CP} = 220 \]

8. **Conclusion**:
- Therefore, the cost price of the item is Rs. 220.