In selling an article for Rs. 76, there is a profit of 52%. If it is sold for Rs. 75, the profit percent will be.

Answer

To solve the problem step by step, we will first determine the cost price (CP) of the article using the information given about the selling price (SP) and the profit percentage. Then, we will calculate the profit percentage when the article is sold for Rs. 75.

### Step 1: Determine the Cost Price (CP)
We know that:
- Selling Price (SP) = Rs. 76
- Profit Percentage = 52%

The formula for Selling Price in terms of Cost Price and Profit Percentage is:
\[ SP = CP + \left( \frac{Profit \%}{100} \times CP \right) \]

This can be rewritten as:
\[ SP = CP + \frac{52}{100} \times CP \]
\[ SP = CP \left(1 + \frac{52}{100}\right) \]
\[ SP = CP \left(\frac{100 + 52}{100}\right) \]
\[ SP = CP \left(\frac{152}{100}\right) \]

Now, substituting the value of SP:
\[ 76 = CP \left(\frac{152}{100}\right) \]

To find CP, we rearrange the equation:
\[ CP = \frac{76 \times 100}{152} \]

Calculating this gives:
\[ CP = \frac{7600}{152} \]
\[ CP = 50 \]

### Step 2: Calculate Profit Percentage when SP = Rs. 75
Now that we have the cost price (CP = Rs. 50), we will find the profit percentage when the selling price is Rs. 75.

The formula for Profit Percentage is:
\[ Profit \% = \left( \frac{Profit}{CP} \right) \times 100 \]

First, we calculate the profit:
\[ Profit = SP - CP \]
\[ Profit = 75 - 50 = 25 \]

Now, substituting the profit into the profit percentage formula:
\[ Profit \% = \left( \frac{25}{50} \right) \times 100 \]
\[ Profit \% = 0.5 \times 100 \]
\[ Profit \% = 50\% \]

### Final Answer
The profit percentage when the article is sold for Rs. 75 is **50%**.

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