`CP = 100/((100+ g a i n %)) xx SP`

Options

A. F
B. T
C. Can not say anything
D. May or may not be true

Answer

To solve the equation \( CP = \frac{100}{(100 + \text{gain \%})} \times SP \), we will follow these steps:

### Step 1: Understand the Variables
- **CP**: Cost Price
- **SP**: Selling Price
- **Gain %**: Profit percentage

### Step 2: Identify the Formula
The formula given is:
\[ CP = \frac{100}{(100 + \text{gain \%})} \times SP \]
This formula helps us calculate the Cost Price when we know the Selling Price and the Gain Percentage.

### Step 3: Rearranging the Formula (if needed)
If we need to find CP, we can directly use the formula as it is. However, if we want to find SP or gain percentage, we may need to rearrange the formula accordingly.

### Step 4: Substitute Values (if provided)
If you have specific values for SP and gain percentage, substitute them into the formula. For example, if SP = 200 and gain % = 20, then:
\[ CP = \frac{100}{(100 + 20)} \times 200 \]

### Step 5: Calculate the Denominator
Calculate the denominator:
\[ 100 + \text{gain \%} = 100 + 20 = 120 \]

### Step 6: Calculate the Fraction
Now, calculate the fraction:
\[ \frac{100}{120} = \frac{5}{6} \]

### Step 7: Multiply by SP
Now, multiply this fraction by the Selling Price:
\[ CP = \frac{5}{6} \times 200 \]

### Step 8: Final Calculation
Calculate the final value:
\[ CP = \frac{5 \times 200}{6} = \frac{1000}{6} \approx 166.67 \]

### Conclusion
The Cost Price (CP) is approximately 166.67.

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