If selling price of an article is ₹638 and profit is 45%, then what will be the net profit?

Options

A. ₹256
B. ₹287.1
C. ₹440
D. ₹198

Answer

To find the net profit when the selling price (SP) of an article is ₹638 and the profit percentage is 45%, we can follow these steps:

### Step 1: Understand the given information
- Selling Price (SP) = ₹638
- Profit Percentage = 45%

### Step 2: Use the formula for Selling Price
The formula for Selling Price in terms of Cost Price (CP) and Profit Percentage is:
\[ SP = CP + \text{Profit} \]
Where Profit can be expressed as:
\[ \text{Profit} = \frac{\text{Profit Percentage}}{100} \times CP \]

### Step 3: Rewrite the Selling Price formula
We can rewrite the Selling Price formula as:
\[ SP = CP + \left(\frac{Profit \%}{100} \times CP\right) \]
This can be simplified to:
\[ SP = CP \left(1 + \frac{Profit \%}{100}\right) \]

### Step 4: Substitute the values
Substituting the known values into the equation:
\[ 638 = CP \left(1 + \frac{45}{100}\right) \]
\[ 638 = CP \left(1 + 0.45\right) \]
\[ 638 = CP \times 1.45 \]

### Step 5: Solve for Cost Price (CP)
To find the Cost Price (CP), we can rearrange the equation:
\[ CP = \frac{638}{1.45} \]
Calculating this gives:
\[ CP = \frac{638}{1.45} \approx 440 \]

### Step 6: Calculate the Profit
Now that we have the Cost Price, we can calculate the Profit:
\[ \text{Profit} = SP - CP \]
\[ \text{Profit} = 638 - 440 \]
\[ \text{Profit} = 198 \]

### Final Answer
The net profit is ₹198.

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