Find CP when SP= rs. 40.60, gain = 16%?

Options

A. a. rs.35
B. b. rs.50
C. c. rs.75
D. d. rs. 89

Answer

To find the Cost Price (CP) when the Selling Price (SP) is Rs. 40.60 and the gain is 16%, we can follow these steps:

### Step 1: Understand the relationship between SP, CP, and Gain
The gain percentage is calculated based on the Cost Price (CP). The formula for Selling Price (SP) in terms of Cost Price (CP) and Gain is:
\[ SP = CP + \text{Gain} \]
Where Gain can be expressed as:
\[ \text{Gain} = \frac{\text{Gain Percentage}}{100} \times CP \]
Thus, we can rewrite the SP formula as:
\[ SP = CP + \left(\frac{Gain \%}{100} \times CP\right) \]
This can be simplified to:
\[ SP = CP \left(1 + \frac{Gain \%}{100}\right) \]

### Step 2: Substitute known values into the formula
Given:
- SP = Rs. 40.60
- Gain % = 16%

Substituting these values into the formula gives:
\[ 40.60 = CP \left(1 + \frac{16}{100}\right) \]
\[ 40.60 = CP \left(1 + 0.16\right) \]
\[ 40.60 = CP \times 1.16 \]

### Step 3: Solve for CP
To find CP, we can rearrange the equation:
\[ CP = \frac{40.60}{1.16} \]

Now, calculating the right-hand side:
\[ CP = \frac{40.60}{1.16} \approx 35 \]

### Conclusion
Thus, the Cost Price (CP) is approximately Rs. 35.

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