A person bought some article at rate of 6 for Rs 20 and bought same number of articles at the rate of 8 for Rs 25. And sold all the stock at the rate of 8 for Rs 31. Find the profit or loss% ?

Answer

To solve the problem, we need to calculate the total cost price (CP) of the articles, the total selling price (SP), and then find the profit or loss percentage.

### Step 1: Calculate the number of articles bought in each transaction
- **First Purchase:** The person bought 6 articles for Rs 20.
- **Second Purchase:** The person bought 8 articles for Rs 25.

Since the question states that the same number of articles were bought in both transactions, we can find a common multiple of 6 and 8. The least common multiple (LCM) of 6 and 8 is 24.

### Step 2: Calculate the number of articles bought in each transaction
- **For the first purchase:**
- To buy 24 articles at the rate of 6 for Rs 20, we calculate how many sets of 6 are in 24:
\[ \text{Number of sets} = \frac{24}{6} = 4 \]
- Total cost for the first purchase:
\[ \text{Total Cost} = 4 \times 20 = Rs 80 \]

- **For the second purchase:**
- To buy 24 articles at the rate of 8 for Rs 25, we calculate how many sets of 8 are in 24:
\[ \text{Number of sets} = \frac{24}{8} = 3 \]
- Total cost for the second purchase:
\[ \text{Total Cost} = 3 \times 25 = Rs 75 \]

### Step 3: Calculate the total cost price (CP)
- Total cost price for all articles:
\[ \text{Total CP} = 80 + 75 = Rs 155 \]

### Step 4: Calculate the total selling price (SP)
- The person sold all 24 articles at the rate of 8 for Rs 31.
- To find the selling price for 24 articles:
\[ \text{Number of sets} = \frac{24}{8} = 3 \]
- Total selling price:
\[ \text{Total SP} = 3 \times 31 = Rs 93 \]

### Step 5: Calculate profit or loss
- To find the profit or loss, we subtract the total cost price from the total selling price:
\[ \text{Profit or Loss} = \text{Total SP} - \text{Total CP} = 93 - 155 = -62 \]
Since the result is negative, it indicates a loss.

### Step 6: Calculate the loss percentage
- The loss percentage is calculated using the formula:
\[ \text{Loss Percentage} = \left( \frac{\text{Loss}}{\text{Total CP}} \right) \times 100 \]
Substituting the values:
\[ \text{Loss Percentage} = \left( \frac{62}{155} \right) \times 100 \approx 40\% \]

### Final Answer
The loss percentage is approximately **40%**.