A person bought some articles at rate of 6 for Rs 5 and sold them at the rate of 5 for Rs 6. Find the profit or loss percent?

Answer

To find the profit or loss percentage for the given question, we will follow these steps:

### Step 1: Determine the Cost Price (CP) of one article
The person bought 6 articles for Rs 5.

To find the cost price of one article:
\[ \text{CP of 1 article} = \frac{5 \text{ Rs}}{6} = \frac{5}{6} \text{ Rs} \]

### Step 2: Determine the Selling Price (SP) of one article
The person sold 5 articles for Rs 6.

To find the selling price of one article:
\[ \text{SP of 1 article} = \frac{6 \text{ Rs}}{5} = \frac{6}{5} \text{ Rs} \]

### Step 3: Calculate the Profit or Loss
Now we will compare the selling price and cost price to determine profit or loss.

- Cost Price (CP) of 1 article = \( \frac{5}{6} \) Rs
- Selling Price (SP) of 1 article = \( \frac{6}{5} \) Rs

To find the profit:
\[ \text{Profit} = \text{SP} - \text{CP} = \frac{6}{5} - \frac{5}{6} \]

### Step 4: Find a common denominator and calculate the profit
The common denominator of 5 and 6 is 30.

Converting both fractions:
\[ \frac{6}{5} = \frac{36}{30} \quad \text{and} \quad \frac{5}{6} = \frac{25}{30} \]

Now, substituting back:
\[ \text{Profit} = \frac{36}{30} - \frac{25}{30} = \frac{11}{30} \text{ Rs} \]

### Step 5: Calculate the Profit Percentage
The profit percentage is calculated using the formula:
\[ \text{Profit Percentage} = \left( \frac{\text{Profit}}{\text{CP}} \right) \times 100 \]

Substituting the values:
\[ \text{Profit Percentage} = \left( \frac{\frac{11}{30}}{\frac{5}{6}} \right) \times 100 \]

### Step 6: Simplify the calculation
To simplify:
\[ \frac{\frac{11}{30}}{\frac{5}{6}} = \frac{11}{30} \times \frac{6}{5} = \frac{66}{150} \]

Now calculating the percentage:
\[ \text{Profit Percentage} = \frac{66}{150} \times 100 = 44\% \]

### Conclusion
The profit percentage is **44%**.

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