Marked price of an article is Rs250 more than cost price of that article and it is sold at a discount of 15% on marked price. Find the cost price of the article if the profit percent earned is 27.5%?

Options

A. Rs 600
B. Rs 550
C. Rs 500
D. Rs 750

Answer

To solve the problem step by step, let's denote the cost price of the article as \( CP \).

### Step 1: Define the Marked Price
According to the problem, the marked price (MP) is Rs 250 more than the cost price. Therefore, we can express the marked price as:
\[ MP = CP + 250 \]

### Step 2: Calculate the Selling Price
The article is sold at a discount of 15% on the marked price. The selling price (SP) can be calculated as:
\[ SP = MP - (15\% \text{ of } MP) \]
This can be rewritten as:
\[ SP = MP \times (1 - 0.15) = MP \times 0.85 \]

### Step 3: Substitute the Marked Price
Substituting the expression for MP from Step 1 into the SP equation:
\[ SP = (CP + 250) \times 0.85 \]

### Step 4: Calculate the Selling Price in Terms of Cost Price and Profit
We know that the profit percentage is 27.5%. The selling price can also be expressed in terms of the cost price:
\[ SP = CP + (27.5\% \text{ of } CP) \]
This can be rewritten as:
\[ SP = CP \times (1 + 0.275) = CP \times 1.275 \]

### Step 5: Set the Two Expressions for Selling Price Equal
Since both expressions represent the selling price, we can set them equal to each other:
\[ (CP + 250) \times 0.85 = CP \times 1.275 \]

### Step 6: Expand and Rearrange the Equation
Expanding the left side:
\[ 0.85CP + 212.5 = 1.275CP \]

Now, rearranging the equation to isolate \( CP \):
\[ 212.5 = 1.275CP - 0.85CP \]
\[ 212.5 = 0.425CP \]

### Step 7: Solve for Cost Price
Now, divide both sides by 0.425 to find the cost price:
\[ CP = \frac{212.5}{0.425} \]
\[ CP = 500 \]

### Conclusion
Thus, the cost price of the article is:
\[ \text{Cost Price} = Rs 500 \]