On selling 100 pens, a man gains the selling price of 20 pens. The gain per cent is

Options

A. 0.2
B. 0.25
C. `16 2/3%`
D. 0.15

Answer

To solve the problem step by step, we will calculate the gain percentage based on the information provided.

### Step 1: Understand the Information Given
We know that:
- Selling 100 pens results in a gain equal to the selling price of 20 pens.

### Step 2: Define Variables
Let:
- Selling Price (SP) of 1 pen = \( x \)
- Therefore, Selling Price (SP) of 100 pens = \( 100x \)
- Gain from selling 100 pens = Selling Price of 20 pens = \( 20x \)

### Step 3: Calculate the Gain
From the information given:
- Gain = Selling Price of 100 pens - Cost Price of 100 pens
- We know that the gain is also equal to the selling price of 20 pens, which is \( 20x \).

### Step 4: Calculate the Cost Price
To find the cost price (CP) of the 100 pens, we can set up the equation:
- Gain = SP of 100 pens - CP of 100 pens
- Therefore, \( 20x = 100x - CP \)
- Rearranging gives us: \( CP = 100x - 20x = 80x \)

### Step 5: Calculate Gain
Now, we can calculate the gain:
- Gain = Selling Price of 100 pens - Cost Price of 100 pens
- Gain = \( 100x - 80x = 20x \)

### Step 6: Calculate Gain Percentage
The formula for gain percentage is:
\[ \text{Gain Percentage} = \left( \frac{\text{Gain}}{\text{Cost Price}} \right) \times 100 \]
Substituting the values we have:
\[ \text{Gain Percentage} = \left( \frac{20x}{80x} \right) \times 100 \]
The \( x \) cancels out:
\[ \text{Gain Percentage} = \left( \frac{20}{80} \right) \times 100 = \frac{1}{4} \times 100 = 25\% \]

### Final Answer
The gain percentage is **25%**.

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