Sure, let's solve this step by step.
Step 1: Find the cost price of the calculator.
Given:
- Selling price (SP) is Rs 230.
- Profit percentage is 15%.
We know the formula for selling price based on cost price and profit percentage:
[tex]\[ \text{Selling Price} = \text{Cost Price} \times \left(1 + \frac{\text{Profit Percentage}}{100}\right) \][/tex]
We need to rearrange this formula to solve for the Cost Price (CP):
[tex]\[ \text{Cost Price} = \frac{\text{Selling Price}}{1 + \frac{\text{Profit Percentage}}{100}} \][/tex]
Substitute the given values into the formula:
[tex]\[ \text{Cost Price} = \frac{230}{1 + \frac{15}{100}} \][/tex]
[tex]\[ \text{Cost Price} = \frac{230}{1 + 0.15} \][/tex]
[tex]\[ \text{Cost Price} = \frac{230}{1.15} \][/tex]
[tex]\[ \text{Cost Price} \approx 200.00 \][/tex]
So, the cost price of the calculator is approximately Rs 200.00.
Step 2: Find the new selling price to make a profit of 10%.
Given:
- Cost Price (CP) is Rs 200.00.
- New profit percentage is 10%.
We use the same formula for selling price:
[tex]\[ \text{Selling Price} = \text{Cost Price} \times \left(1 + \frac{\text{New Profit Percentage}}{100}\right) \][/tex]
Substitute the cost price and the new profit percentage into the formula:
[tex]\[ \text{Selling Price} = 200.00 \times \left(1 + \frac{10}{100}\right) \][/tex]
[tex]\[ \text{Selling Price} = 200.00 \times 1.1 \][/tex]
[tex]\[ \text{Selling Price} = 220.00 \][/tex]
So, to make a profit of 10%, the calculator must be sold at Rs 220.00.
