When Vijay sells 12 pens, he gains the selling price of 2 pens . Calculate his `%` profit
A. `15%`
B. `20%`
C.`18%`
D. `12%`

Options

A. C
B. A
C. B
D. D

Answer

To solve the problem step by step, let's break it down:

### Step 1: Understand the Selling Price
Let the selling price of one pen be \( X \).

### Step 2: Calculate the Selling Price of 12 Pens
If Vijay sells 12 pens, the total selling price (SP) for 12 pens is:
\[ SP = 12 \times X = 12X \]

### Step 3: Determine the Profit
According to the problem, when Vijay sells 12 pens, he gains the selling price of 2 pens. Therefore, the profit (P) is:
\[ P = 2 \times X = 2X \]

### Step 4: Calculate the Cost Price
The cost price (CP) can be calculated using the formula:
\[ CP = SP - P \]
Substituting the values we have:
\[ CP = 12X - 2X = 10X \]

### Step 5: Calculate the Profit Percentage
The profit percentage is given by the formula:
\[ \text{Profit Percentage} = \left( \frac{P}{CP} \right) \times 100 \]
Substituting the values of profit and cost price:
\[ \text{Profit Percentage} = \left( \frac{2X}{10X} \right) \times 100 \]

### Step 6: Simplify the Expression
Cancelling \( X \) from the numerator and denominator:
\[ \text{Profit Percentage} = \left( \frac{2}{10} \right) \times 100 = 20\% \]

### Conclusion
Thus, the percentage profit is \( 20\% \), which corresponds to option B.

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