On selling 80 articles for Rs 140 a person incurred a loss of 30%. How many articles he should sell for Rs 104 to earn profit of 30%.

Answer

To solve the problem step by step, we will follow the logic presented in the video transcript.

### Step-by-Step Solution:

1. **Understand the Loss Situation**:
- The person sold 80 articles for Rs 140 and incurred a loss of 30%.
- This means that the selling price (SP) is 70% of the cost price (CP) because the loss is 30%.

2. **Calculate the Cost Price (CP)**:
- Let the cost price of 80 articles be CP.
- Since the selling price is 70% of the cost price:
\[ SP = 70\% \times CP \]
\[ 140 = 0.7 \times CP \]
- To find CP, we rearrange the equation:
\[ CP = \frac{140}{0.7} = 200 \]
- Therefore, the cost price of 80 articles is Rs 200.

3. **Calculate the Cost Price per Article**:
- To find the cost price per article:
\[ CP \text{ per article} = \frac{200}{80} = 2.5 \]

4. **Understand the Profit Situation**:
- Now, we need to find out how many articles should be sold for Rs 104 to earn a profit of 30%.
- A profit of 30% means the selling price will be 130% of the cost price.

5. **Calculate the Selling Price (SP) for Profit**:
- Let the number of articles sold be \( x \).
- The selling price for \( x \) articles is Rs 104, and we want this to be 130% of the cost price:
\[ SP = 130\% \times CP \text{ per article} \]
\[ SP = 1.3 \times 2.5 = 3.25 \text{ (cost price per article)} \]

6. **Set Up the Equation**:
- The total selling price for \( x \) articles is:
\[ 104 = x \times 3.25 \]

7. **Solve for \( x \)**:
- Rearranging gives:
\[ x = \frac{104}{3.25} = 32 \]

### Conclusion:
The person should sell **32 articles** for Rs 104 to earn a profit of 30%.