The marked price of an article is Rs 840. A shopkeeper gives a discount of 40% and still makes a profit of 5%. What is the cost price (in Rs) of the article?

Options

A. 480
B. 360
C. 420
D. 400

Answer

To find the cost price (CP) of the article given the marked price (MP), discount percentage, and profit percentage, we can follow these steps:

1. **Identify the given values:**
- Marked Price (MP) = Rs 840
- Discount = 40%
- Profit = 5%

2. **Calculate the selling price (SP) after discount:**
- The selling price can be calculated using the formula:
\[ SP = MP - \text{Discount} \]
- First, calculate the discount amount:
\[ \text{Discount Amount} = \frac{40}{100} \times 840 = 0.4 \times 840 = Rs 336 \]
- Now, calculate the selling price:
\[ SP = 840 - 336 = Rs 504 \]

3. **Relate selling price to cost price using profit percentage:**
- The selling price is also related to the cost price by the profit percentage:
\[ SP = CP + \text{Profit} \]
- The profit can be calculated as:
\[ \text{Profit} = \frac{5}{100} \times CP = 0.05 \times CP \]
- Therefore, we can rewrite the equation as:
\[ SP = CP + 0.05 \times CP = 1.05 \times CP \]
- Substituting the selling price we calculated:
\[ 504 = 1.05 \times CP \]

4. **Solve for the cost price (CP):**
- Rearranging the equation gives:
\[ CP = \frac{504}{1.05} \]
- Now, calculate the cost price:
\[ CP = 480 \]

Thus, the cost price of the article is Rs 480.