To determine the cost price of a calculator that is sold for Rs 230 at a profit of 15%, we can follow these steps:
1. Identify the selling price (SP): The selling price of the calculator is given as Rs 230.
2. Identify the profit percentage: The profit made on the sale is 15%.
3. Understand the relationship between cost price (CP), selling price (SP), and profit:
The selling price (SP) can be expressed as the cost price (CP) plus the profit. The profit is a percentage of the cost price.
4. Write the formula for the selling price in terms of the cost price and profit percentage:
[tex]\[
\text{Selling Price (SP)} = \text{Cost Price (CP)} + \text{Profit}
\][/tex]
Here, Profit can be written as:
[tex]\[
\text{Profit} = \left(\frac{\text{Profit Percent}}{100}\right) \times \text{Cost Price (CP)}
\][/tex]
5. Substitute the profit expression into the formula for SP:
[tex]\[
\text{SP} = \text{CP} + \left(\frac{\text{Profit Percent}}{100}\right) \times \text{CP}
\][/tex]
[tex]\[
\text{SP} = \text{CP} \times \left(1 + \frac{\text{Profit Percent}}{100}\right)
\][/tex]
6. Plug in the given values:
- SP = 230
- Profit Percent = 15
[tex]\[
230 = \text{CP} \times \left(1 + \frac{15}{100}\right)
\][/tex]
[tex]\[
230 = \text{CP} \times \left(1 + 0.15\right)
\][/tex]
[tex]\[
230 = \text{CP} \times 1.15
\][/tex]
7. Solve for the cost price (CP):
[tex]\[
\text{CP} = \frac{230}{1.15}
\][/tex]
[tex]\[
\text{CP} \approx 200.00000000000003
\][/tex]
So, the cost price of the calculator is approximately Rs 200.
