Rashmi sold an article at a loss of `10%`. If she had sold the article for Rs 90 more, she would have received a gain of `10%`. Find the cost price of the article

Options

A. Rs 475
B. Rs 460
C. Rs 420
D. Rs 450

Answer

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

### Step 1: Understanding the Selling Price at Loss
Rashmi sold the article at a loss of 10%. Therefore, the selling price (SP) when sold at a loss can be expressed as:
\[ SP_1 = CP - 0.10 \times CP = 0.90 \times CP \]

### Step 2: Understanding the Selling Price at Gain
If she had sold the article for Rs 90 more, she would have received a gain of 10%. The selling price in this case can be expressed as:
\[ SP_2 = CP + 0.10 \times CP = 1.10 \times CP \]
According to the problem, we know that:
\[ SP_2 = SP_1 + 90 \]

### Step 3: Substitute the Selling Prices
Now, substituting the expressions for \( SP_1 \) and \( SP_2 \):
\[ 1.10 \times CP = 0.90 \times CP + 90 \]

### Step 4: Rearranging the Equation
Rearranging the equation gives:
\[ 1.10 \times CP - 0.90 \times CP = 90 \]
\[ 0.20 \times CP = 90 \]

### Step 5: Solving for Cost Price
Now, divide both sides by 0.20 to find \( CP \):
\[ CP = \frac{90}{0.20} = 450 \]

### Conclusion
Thus, the cost price of the article is:
\[ \boxed{450} \]