The selling price of 6 pen is equal to cost price of 4 pen. Find the profit percent?

Let the cost price of one pen be \( C \). Therefore, the cost price of 4 pens is \( 4C \).

The selling price of 6 pens is given to be equal to the cost price of 4 pens. Hence, the selling price of 6 pens is also \( 4C \).

Now, the selling price of one pen is:

\[
\text{Selling Price of 1 pen} = \frac{4C}{6} = \frac{2C}{3}
\]

The profit per pen is the difference between the selling price and the cost price:

\[
\text{Profit per pen} = \frac{2C}{3} - C = \frac{2C - 3C}{3} = \frac{-C}{3}
\]

Now, the profit percentage is calculated as:

\[
\text{Profit Percentage} = \frac{\text{Profit}}{\text{Cost Price}} \times 100
\]

Substituting the values:

\[
\text{Profit Percentage} = \frac{\frac{-C}{3}}{C} \times 100 = -\frac{1}{3} \times 100 = -33.33\%
\]

Therefore, the **loss percentage** is 33.33%.

Would you like further details or have any questions?

Here are 5 related questions to expand on this:
1. How does the relation between selling price and cost price affect profit?
2. What is the significance of calculating profit or loss percentage?
3. How would the profit percentage change if the selling price of 6 pens was higher?
4. What happens if cost price and selling price are equal?
5. How can you apply this formula to different quantities?

**Tip:** Always compare the selling price and cost price directly to quickly identify profit or loss.

The selling price of 6 pens is equal to the cost price of 4 pens. Find the profit percent?

This problem demonstrates how to calculate profit or loss percentage when the selling price of 6 pens is equal to the cost price of 4 pens. Explore key mathematical concepts like profit and loss, ratios, and the relevant formulas used in the solution. Suitable for students in Grades 6-8.

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