The difference between the selling prices of an article sold at 4% and 3% profits is Rs. 3. The cost price of the article is:

Options

A. 1. 400
B. 2. 350
C. 3. 300
D. 4. 100

Answer

To solve the problem step by step, we will follow these steps:

### Step 1: Understand the Selling Price Formula
The selling price (SP) can be calculated using the formula:
\[ \text{SP} = \text{CP} + \text{Profit} \]
Where CP is the cost price and Profit is calculated as a percentage of CP.

### Step 2: Define Selling Prices at Different Profit Percentages
Let the cost price of the article be \( CP \).

- Selling Price at 4% profit:
\[ SP_1 = CP + 0.04 \times CP = CP(1 + 0.04) = CP \times 1.04 \]

- Selling Price at 3% profit:
\[ SP_2 = CP + 0.03 \times CP = CP(1 + 0.03) = CP \times 1.03 \]

### Step 3: Set Up the Equation for the Difference in Selling Prices
According to the problem, the difference between the two selling prices is Rs. 3:
\[ SP_1 - SP_2 = 3 \]

Substituting the expressions for \( SP_1 \) and \( SP_2 \):
\[ CP \times 1.04 - CP \times 1.03 = 3 \]

### Step 4: Simplify the Equation
Factor out \( CP \):
\[ CP(1.04 - 1.03) = 3 \]
\[ CP(0.01) = 3 \]

### Step 5: Solve for Cost Price
Now, divide both sides by 0.01 to find the cost price:
\[ CP = \frac{3}{0.01} = 300 \]

### Conclusion
The cost price of the article is Rs. 300.

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