If the cost price of 8 pens is same as the selling price of 6 pens, then the gain percent is

Options

A. `33(1)/(3)%`
B. `11(1)/(2)%`
C. `13(1)/(3)%`
D. `25%`

Answer

To find the gain percent when the cost price of 8 pens is equal to the selling price of 6 pens, we can follow these steps:

### Step-by-step Solution:

1. **Define Variables**:
Let the cost price (CP) of one pen be \( x \). Therefore, the cost price of 8 pens will be \( 8x \).

2. **Selling Price Calculation**:
According to the problem, the cost price of 8 pens is equal to the selling price (SP) of 6 pens. Therefore, we can write:
\[ 8x = SP \text{ of 6 pens} \]
Let the selling price of one pen be \( y \). Thus, the selling price of 6 pens will be \( 6y \).

3. **Set Up the Equation**:
From the above relationship, we can set up the equation:
\[ 8x = 6y \]

4. **Find the Selling Price per Pen**:
Rearranging the equation to find \( y \):
\[ y = \frac{8x}{6} = \frac{4x}{3} \]

5. **Calculate Profit**:
The profit made on one pen is given by:
\[ \text{Profit} = SP - CP = y - x = \frac{4x}{3} - x \]
To simplify:
\[ \text{Profit} = \frac{4x}{3} - \frac{3x}{3} = \frac{x}{3} \]

6. **Calculate Gain Percent**:
The gain percent is calculated using the formula:
\[ \text{Gain Percent} = \left( \frac{\text{Profit}}{\text{CP}} \right) \times 100 \]
Substituting the values we have:
\[ \text{Gain Percent} = \left( \frac{\frac{x}{3}}{x} \right) \times 100 = \frac{1}{3} \times 100 = 33.33\% \]

7. **Final Answer**:
Therefore, the gain percent is \( 33 \frac{1}{3} \% \).