If an article is sold at a gain of 6% instead of at a loss of 6%, then the seller gets ? 6 more. The cost price of the article is

Options

A. ₹106
B. ₹ 50
C. ₹ 94
D. ₹ 100

Answer

To solve the problem step by step, we will follow the reasoning laid out in the video transcript:

### Step-by-Step Solution:

1. **Understanding the Problem**:
We know that if an article is sold at a gain of 6% instead of a loss of 6%, the seller gets Rs 6 more. We need to find the cost price (CP) of the article.

2. **Setting Up the Variables**:
Let the cost price of the article be Rs X.

3. **Calculating Selling Price with Profit**:
When sold at a gain of 6%, the selling price (SP1) can be calculated as:
\[ SP1 = CP + 6\% \text{ of } CP = CP \times \left(1 + \frac{6}{100}\right) = X \times \frac{106}{100} = \frac{106X}{100} \]

4. **Calculating Selling Price with Loss**:
When sold at a loss of 6%, the selling price (SP2) can be calculated as:
\[ SP2 = CP - 6\% \text{ of } CP = CP \times \left(1 - \frac{6}{100}\right) = X \times \left(1 - \frac{6}{100}\right) = X \times \frac{94}{100} = \frac{94X}{100} \]

5. **Setting Up the Equation**:
According to the problem, the difference between these two selling prices is Rs 6:
\[ SP1 - SP2 = 6 \]
Substituting the expressions for SP1 and SP2:
\[ \frac{106X}{100} - \frac{94X}{100} = 6 \]

6. **Simplifying the Equation**:
Combine the fractions:
\[ \frac{106X - 94X}{100} = 6 \]
This simplifies to:
\[ \frac{12X}{100} = 6 \]

7. **Solving for X**:
To find X, multiply both sides by 100:
\[ 12X = 600 \]
Now, divide both sides by 12:
\[ X = \frac{600}{12} = 50 \]

8. **Conclusion**:
The cost price of the article is Rs 50.

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

---