Find the CP when SP is Rs. 40 and gain is 15%.

Answer

To find the Cost Price (CP) when the Selling Price (SP) is Rs. 40 and the gain is 15%, we can follow these steps:

### Step 1: Understand the relationship between SP, CP, and Gain Percentage
The relationship can be defined using the formula:
\[ \text{SP} = \text{CP} + \text{Gain} \]
Where:
- Gain = Gain Percentage of CP

### Step 2: Express Gain in terms of CP
The gain can also be expressed as:
\[ \text{Gain} = \frac{\text{Gain Percentage}}{100} \times \text{CP} \]
Thus, we can rewrite the SP formula as:
\[ \text{SP} = \text{CP} + \left(\frac{\text{Gain Percentage}}{100} \times \text{CP}\right) \]
This can be simplified to:
\[ \text{SP} = \text{CP} \left(1 + \frac{\text{Gain Percentage}}{100}\right) \]

### Step 3: Rearranging to find CP
We can rearrange the formula to solve for CP:
\[ \text{CP} = \frac{\text{SP}}{1 + \frac{\text{Gain Percentage}}{100}} \]

### Step 4: Substitute the values
Given:
- SP = Rs. 40
- Gain Percentage = 15%

Substituting these values into the formula:
\[ \text{CP} = \frac{40}{1 + \frac{15}{100}} \]
\[ \text{CP} = \frac{40}{1 + 0.15} \]
\[ \text{CP} = \frac{40}{1.15} \]

### Step 5: Calculate the CP
Now, performing the division:
\[ \text{CP} = \frac{40}{1.15} \approx 34.78 \]

### Conclusion
Thus, the Cost Price (CP) is approximately Rs. 34.78.

---