An article was sold for ₹4,000. Had a discount of 10% was being offered, the profit would have been 20%. The cost price of the article was:

Options

A. ₹3,200
B. ₹3,310
C. ₹3,000
D. ₹3,600

Answer

To find the cost price of the article, we can follow these steps:

1. **Understand the Selling Price and Discount**:
The article is sold for ₹4,000. If a discount of 10% is applied, the selling price after the discount would be calculated as follows:
\[ \text{Discount} = 10\% \text{ of Selling Price} \]
\[ \text{Selling Price after discount} = \text{Original Selling Price} - \text{Discount} \]

2. **Calculate the Selling Price After Discount**:
Let the marked price (original selling price) be \( SP \). The selling price after a 10% discount would be:
\[ SP - 0.10 \times SP = 0.90 \times SP \]
Given that the selling price after discount is ₹4,000, we can set up the equation:
\[ 0.90 \times SP = 4000 \]

3. **Solve for the Marked Price (SP)**:
To find \( SP \), divide both sides of the equation by 0.90:
\[ SP = \frac{4000}{0.90} = \frac{4000 \times 100}{90} = \frac{400000}{90} \approx 4444.44 \]

4. **Understanding Profit**:
We are told that if the discount was applied, the profit would be 20%. This means that the selling price after the discount (which is ₹4,000) represents 120% of the cost price (CP):
\[ 4000 = 120\% \text{ of CP} \]
This can be expressed as:
\[ 4000 = \frac{120}{100} \times CP \]

5. **Solve for Cost Price (CP)**:
Rearranging the equation to find the cost price:
\[ CP = \frac{4000 \times 100}{120} = \frac{400000}{120} \approx 3333.33 \]

Thus, the cost price of the article is approximately ₹3,333.33.