the cost price of 20 article is the same as the selling as the selling price of x articles if the profit is 25% find the value of x??

Let's denote:

- \( \text{Cost Price (CP)} \) of each article as \( C \).
- \( \text{Selling Price (SP)} \) of each article as \( S \).
- Profit = 25%.

We are given that the cost price of 20 articles is the same as the selling price of \( x \) articles. Therefore, we can write the equation:

\[
20 \times C = x \times S
\]

Since profit is 25%, the selling price \( S \) is related to the cost price \( C \) as:

\[
S = C + 25\% \text{ of } C = C + 0.25C = 1.25C
\]

Now, substitute \( S = 1.25C \) into the equation:

\[
20 \times C = x \times 1.25C
\]

Simplify by dividing both sides by \( C \) (assuming \( C \neq 0 \)):

\[
20 = 1.25x
\]

Solve for \( x \):

\[
x = \frac{20}{1.25} = 16
\]

Thus, the value of \( x \) is \( \boxed{16} \).

Would you like more details on this, or do you have any questions?

Here are 5 related questions to expand on this concept:

1. If the profit percentage was 30% instead of 25%, what would the value of \( x \) be?
2. How would the value of \( x \) change if the number of articles purchased increased to 25?
3. If the selling price per article was given, how could we calculate the cost price?
4. How would you calculate the profit if you knew the selling price and cost price directly?
5. What would happen if there was a 10% loss instead of a profit?

**Tip:** Always remember that the selling price is calculated by adding the profit percentage to the cost price when dealing with profit-based questions.

This problem involves finding the value of x when the cost price of 20 articles equals the selling price of x articles, with a 25% profit margin. Learn how to set up and solve the algebraic equation using profit and percentage concepts. Suitable for Grades 8-10.

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