If an article is sold at a gain of 5% Instead of being sold at a loss of 5%, one gets 5 more. What is the cost price of the article?

Options

A. 100
B. 3`
C. 50
D. 110

Answer

To solve the problem step by step, we can follow these calculations:

### Step 1: Understand the Problem
We know that selling the article at a gain of 5% gives us 5 more than selling it at a loss of 5%. We need to find the cost price (CP) of the article.

### Step 2: Define the Cost Price
Let the cost price of the article be \( CP \).

### Step 3: Calculate Selling Prices
1. **Selling Price at 5% Gain**:
\[ SP_{gain} = CP + 5\% \text{ of } CP = CP + 0.05 \times CP = 1.05 \times CP \]

2. **Selling Price at 5% Loss**:
\[ SP_{loss} = CP - 5\% \text{ of } CP = CP - 0.05 \times CP = 0.95 \times CP \]

### Step 4: Set Up the Equation
According to the problem, the difference between the selling price at gain and the selling price at loss is 5:
\[ SP_{gain} - SP_{loss} = 5 \]
Substituting the expressions we found:
\[ 1.05 \times CP - 0.95 \times CP = 5 \]

### Step 5: Simplify the Equation
Combine like terms:
\[ (1.05 - 0.95) \times CP = 5 \]
\[ 0.10 \times CP = 5 \]

### Step 6: Solve for Cost Price
To find \( CP \), divide both sides by 0.10:
\[ CP = \frac{5}{0.10} = 50 \]

### Conclusion
The cost price of the article is \( \text{Rs. } 50 \).

---