If a person has sold an article for Rs. 1,300 and made a profit of 30%, find the cost price of the article.

Options

A. Rs. 1,000
B. Rs. 1,200
C. Rs. 1,250
D. Rs. 1,100

Answer

To find the cost price of the article when the selling price and profit percentage are given, we can follow these steps:

### Step 1: Understand the relationship between Selling Price (SP), Cost Price (CP), and Profit Percentage
The formula relating these three is:
\[ \text{SP} = \text{CP} + \text{Profit} \]
Where:
- Profit can also be expressed in terms of CP and profit percentage:
\[ \text{Profit} = \text{CP} \times \left(\frac{\text{Profit Percentage}}{100}\right) \]

### Step 2: Substitute the known values into the formula
Given:
- Selling Price (SP) = Rs. 1,300
- Profit Percentage = 30%

Using the profit formula:
\[ \text{SP} = \text{CP} + \left(\text{CP} \times \frac{30}{100}\right) \]

### Step 3: Simplify the equation
This can be rewritten as:
\[ \text{SP} = \text{CP} + 0.3 \times \text{CP} \]
\[ \text{SP} = 1.3 \times \text{CP} \]

### Step 4: Rearrange the equation to find CP
Now, we can rearrange the equation to solve for CP:
\[ \text{CP} = \frac{\text{SP}}{1.3} \]

### Step 5: Substitute the value of SP
Now substitute SP = 1,300 into the equation:
\[ \text{CP} = \frac{1300}{1.3} \]

### Step 6: Calculate CP
Calculating the above expression:
\[ \text{CP} = 1000 \]

### Conclusion
The cost price of the article is Rs. 1,000.