If a person sells a ‘Saree’ for Rs. 5200,making a profit of 30%,then the cost price of the saree isRs. 4420Rs. 4000Rs. 3900Rs. 3800

1. Break Down the Problem

We need to find the cost price (CP) of the saree given that it is sold for Rs. 5200 at a profit of 30%. The first step will be to understand the relationship between selling price (SP), cost price (CP), and profit percentage.

2. Relevant Concepts

The profit percentage can be expressed with the formula:

$\text{Profit} = \text{Selling Price} - \text{Cost Price}$

The profit percentage also relates to cost price as follows:

$\text{Profit Percentage} = \left(\frac{\text{Profit}}{\text{Cost Price}}\right) \times 100$

We can rearrange this to express Selling Price in terms of Cost Price:

$\text{Selling Price} = \text{Cost Price} + \left(\frac{\text{Profit Percentage}}{100} \times \text{Cost Price}\right)$

This can be simplified to:

$\text{Selling Price} = \text{Cost Price} \times \left(1 + \frac{\text{Profit Percentage}}{100}\right)$

3. Analysis and Detail

Let's denote $CP$ as the cost price. According to the problem:

• Selling Price, $SP = 5200$
• Profit Percentage = 30%

Now, we can substitute these values into the equation:

$5200 = CP \times \left(1 + \frac{30}{100}\right)$

This simplifies to:

$5200 = CP \times \left(1 + 0.3\right)$ $5200 = CP \times 1.3$

Now, to find $CP$:

$CP = \frac{5200}{1.3}$

4. Verify and Summarize

Now we perform the calculation:

$CP = \frac{5200}{1.3} = 4000$

Thus, we find that the cost price of the saree is Rs. 4000.

Final Answer

The cost price of the saree is Rs. 4000.