If the cost price of 12 pens is equal to the selling price of 8 pens, then the gain percent is
A. 33 % B. 66% C. 25% D. 50%
Correct Answer: D
Explanation
To find the gain percent, we can follow these steps:
1. Define Variables: - Let the cost price (CP) of 1 pen be \( C \). - Let the selling price (SP) of 1 pen be \( S \).
2. Use the Given Information: - The cost price of 12 pens is equal to the selling price of 8 pens. \[ 12C = 8S \] - Solve for \( S \) in terms of \( C \): \[ S = \frac{12C}{8} = \frac{3C}{2} \]
3. Calculate the Gain per Pen: - Gain per pen is \( S - C \): \[ \text{Gain} = \frac{3C}{2} - C = \frac{3C - 2C}{2} = \frac{C}{2} \]
4. Calculate the Gain Percent: - Gain percent is calculated as: \[ \text{Gain Percent} = \left(\frac{\text{Gain}}{\text{CP}}\right) \times 100\% \] \[ \text{Gain Percent} = \left(\frac{\frac{C}{2}}{C}\right) \times 100\% = \frac{1}{2} \times 100\% = 50\% \]