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If the cost price of 12 pens is equal to the selling price of 8 pens, then the gain ...

If the cost price of 12 pens is equal to the selling price of 8 pens, then the gain percent is
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  • A 33 %
  • B 66%
  • C 25%
  • D 50%
Correct Answer: Option 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:
\[
\text{Gain Percent} = \left(\frac{\text{Gain}}{\text{CP}}\right) \times 100\%
\]
\[
\text{Gain Percent} = \left(\frac{\frac{C}{2}}{C}\right) \times 100\% = \frac{1}{2} \times 100\% = 50\%
\]


The gain percent is 50%.

The correct answer is D. 50%.

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