If an article is sold at 5% gain instead of 5% loss, the man gains 5 more. Find the cost price of that article

Options

A. 100
B. 105
C. 50
D. 110

Answer

To solve the problem, we need to determine the cost price (CP) of the article based on the information given about profit and loss.

### Step-by-Step Solution:

1. **Understand the Problem**:
- The article is sold at a 5% gain instead of a 5% loss.
- This change results in an additional gain of 5 units (currency).

2. **Define Variables**:
- Let the cost price (CP) of the article be \( x \).

3. **Calculate Selling Price with Loss**:
- If the article is sold at a 5% loss, the selling price (SP) can be calculated as:
\[ SP_{\text{loss}} = CP - (5\% \text{ of } CP) = x - 0.05x = 0.95x \]

4. **Calculate Selling Price with Gain**:
- If the article is sold at a 5% gain, the selling price (SP) can be calculated as:
\[ SP_{\text{gain}} = CP + (5\% \text{ of } CP) = x + 0.05x = 1.05x \]

5. **Set Up the Equation**:
- According to the problem, the difference between the selling price at gain and the selling price at loss is 5 units:
\[ SP_{\text{gain}} - SP_{\text{loss}} = 5 \]
- Substituting the values we calculated:
\[ 1.05x - 0.95x = 5 \]

6. **Simplify the Equation**:
- Combine like terms:
\[ 0.10x = 5 \]

7. **Solve for Cost Price (CP)**:
- To find \( x \), divide both sides by 0.10:
\[ x = \frac{5}{0.10} = 50 \]

8. **Conclusion**:
- The cost price of the article is \( \text{Rs. } 50 \).

### Final Answer:
The cost price of the article is Rs. 50.