What is the cost price of a product, if the gain in selling it for Rs. 27,120 is 13% ?

Options

A. Rs 24,600
B. Rs 24,000
C. Rs 22,800
D. Rs, 25,300

Answer

To find the cost price (CP) of a product when the selling price (SP) is Rs. 27,120 and the gain is 13%, we can follow these steps:

### Step-by-Step Solution:

1. **Understand the relationship between SP, CP, and Profit Percentage**:
The selling price (SP) can be expressed in terms of the cost price (CP) and the profit percentage. The formula is:
\[ SP = CP + \text{Profit} \]
where Profit can be calculated as:
\[ \text{Profit} = \frac{\text{Profit Percentage}}{100} \times CP \]

2. **Set up the equation**:
Given that the profit percentage is 13%, we can write:
\[ SP = CP + \frac{13}{100} \times CP \]
This simplifies to:
\[ SP = CP \left(1 + \frac{13}{100}\right) = CP \left(\frac{113}{100}\right) \]

3. **Substitute the given SP**:
We know that SP = Rs. 27,120. Therefore, we can set up the equation:
\[ 27120 = CP \left(\frac{113}{100}\right) \]

4. **Solve for CP**:
To isolate CP, we can rearrange the equation:
\[ CP = 27120 \times \frac{100}{113} \]

5. **Calculate CP**:
Now we perform the calculation:
\[ CP = \frac{27120 \times 100}{113} \]
\[ CP = \frac{2712000}{113} \approx 24000 \]

6. **Final Answer**:
Therefore, the cost price (CP) of the product is Rs. 24,000.