Calculate the profit margin if x in the previous question equal 207

a. 20%

b. 16.67%

c. 35%

d. 31.25%

What's the correct answer 

To calculate the profit margin given that \( x = 207 \), we will follow these steps:

### Step 1: Set Up the Equation
Given that the cost price of 20 articles equals the selling price of \( x \) articles, the equation is:
\[
20C = 207S
\]
Where:
- \( C \) is the cost price of one article.
- \( S \) is the selling price of one article.

### Step 2: Express the Selling Price in Terms of Cost Price
The selling price \( S \) can be expressed as:
\[
S = C + \text{Profit}
\]
The profit margin \( P \) is defined as:
\[
\text{Profit Margin} = \frac{S - C}{C} \times 100\%
\]
Let's represent the selling price \( S \) in terms of the profit margin \( P \):
\[
S = C + \frac{P}{100} \times C = \left(1 + \frac{P}{100}\right)C
\]

### Step 3: Substitute \( S \) in the Original Equation
Substitute \( S = \left(1 + \frac{P}{100}\right)C \) into the equation \( 20C = 207S \):
\[
20C = 207 \left(1 + \frac{P}{100}\right)C
\]

### Step 4: Simplify and Solve for \( P \)
Cancel out \( C \) from both sides (assuming \( C \) is not zero):
\[
20 = 207 \left(1 + \frac{P}{100}\right)
\]

Now, solve for \( P \):
\[
1 + \frac{P}{100} = \frac{20}{207}
\]

\[
\frac{P}{100} = \frac{20}{207} - 1 = \frac{20 - 207}{207} = \frac{-187}{207}
\]

This leads to:
\[
P = -100 \times \frac{187}{207} = -90.34
\]

This result is incorrect because it implies a loss instead of a profit. Instead, there was an algebraic mistake. Let's redo the calculation:

We should have:

\[
1 + \frac{P}{100} = \frac{20}{207}
\]

Thus:

\[
\frac{P}{100} = \frac{20}{207} - 1 = \frac{20 - 207}{207} = \frac{-187}{207}
]

Giving P as -90.34%. Since this isn’t one of the answers, there’s likely an error in the way I rewrote it. 

The actual answer isn’t close to those options.

Would you like a detailed reworking? The four questions are:
1. How do you interpret different profit margins?
2. Could you see another similar problem?
3. How might we recalculate other factors?
4. What happens when taxes change the problem?

**Tip:** Always carefully check profit-related calculations.

Learn how to calculate the profit margin when given that the selling price of 207 articles equals the cost price of 20 articles. Follow a detailed step-by-step solution involving profit margin formula and algebraic equations.

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