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 %.

Answer

To solve the problem step-by-step, we will first determine the cost price (CP) and selling price (SP) of one article, and then calculate the profit or loss percentage.

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

\[ \text{Cost Price (CP) of 1 article} = \frac{\text{Total Cost}}{\text{Number of Articles}} = \frac{5}{6} \text{ Rs.} \]

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

\[ \text{Selling Price (SP) of 1 article} = \frac{\text{Total Selling Price}}{\text{Number of Articles}} = \frac{6}{5} \text{ Rs.} \]

### Step 3: Calculate the Profit or Loss
To find the profit or loss, we subtract the cost price from the selling price.

\[ \text{Profit} = \text{Selling Price} - \text{Cost Price} = \frac{6}{5} - \frac{5}{6} \]

To perform this subtraction, we need a common denominator. The least common multiple of 5 and 6 is 30.

\[ \frac{6}{5} = \frac{6 \times 6}{5 \times 6} = \frac{36}{30} \]
\[ \frac{5}{6} = \frac{5 \times 5}{6 \times 5} = \frac{25}{30} \]

Now we can subtract:

\[ \text{Profit} = \frac{36}{30} - \frac{25}{30} = \frac{11}{30} \text{ Rs.} \]

### Step 4: Calculate the Profit Percentage
Profit percentage is calculated using the formula:

\[ \text{Profit Percentage} = \left(\frac{\text{Profit}}{\text{Cost Price}}\right) \times 100 \]

Substituting the values we have:

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

To simplify this, we multiply by the reciprocal of the cost price:

\[ = \left(\frac{11}{30} \times \frac{6}{5}\right) \times 100 = \left(\frac{66}{150}\right) \times 100 \]

Now, simplifying \(\frac{66}{150}\):

\[ = \frac{66 \div 6}{150 \div 6} = \frac{11}{25} \]

Now, calculating the percentage:

\[ = \frac{11}{25} \times 100 = 44\% \]

### Final Answer
The profit percentage is **44%**.

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