The selling price of 20 articles is equal to the cost price of 22 articles. The gain percentage is

Options

A. `12%`
B. `9%`
C. `10%`
D. `11%`

Answer

To solve the problem step by step, we will follow these calculations:

### Step 1: Understand the relationship between selling price and cost price
The problem states that the selling price (SP) of 20 articles is equal to the cost price (CP) of 22 articles. We can express this mathematically as:
\[ SP_{20} = CP_{22} \]

### Step 2: Define the selling price and cost price
Let the cost price of one article be \( CP = X \). Therefore, the total cost price of 22 articles is:
\[ CP_{22} = 22X \]
Similarly, let the selling price of one article be \( SP = Y \). Thus, the total selling price of 20 articles is:
\[ SP_{20} = 20Y \]

### Step 3: Set up the equation
From the relationship established in Step 1:
\[ 20Y = 22X \]

### Step 4: Find the selling price of one article
To find the selling price of one article, we can rearrange the equation:
\[ Y = \frac{22X}{20} = \frac{11X}{10} \]

### Step 5: Calculate the gain for one article
The gain for one article can be calculated as:
\[ \text{Gain} = SP - CP = Y - X \]
Substituting the value of \( Y \):
\[ \text{Gain} = \frac{11X}{10} - X \]
To simplify this, we can write \( X \) as \( \frac{10X}{10} \):
\[ \text{Gain} = \frac{11X}{10} - \frac{10X}{10} = \frac{X}{10} \]

### Step 6: Calculate the gain percentage
The gain percentage is calculated using the formula:
\[ \text{Gain Percentage} = \left( \frac{\text{Gain}}{CP} \right) \times 100 \]
Substituting the values we have:
\[ \text{Gain Percentage} = \left( \frac{\frac{X}{10}}{X} \right) \times 100 \]
This simplifies to:
\[ \text{Gain Percentage} = \left( \frac{1}{10} \right) \times 100 = 10\% \]

### Conclusion
The gain percentage is **10%**.

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