Step 1: Understanding the Question:
The question provides a relationship between the selling price (SP) of a certain number of articles and the cost price (CP) of another number of articles. We need to calculate the overall gain percentage from this transaction.
Step 2: Key Formula or Approach:
The formula for gain percentage is:
\[
\text{Gain \%} = \left( \frac{\text{Selling Price} - \text{Cost Price}}{\text{Cost Price}} \right) \times 100
\]
Or more simply:
\[
\text{Gain \%} = \left( \frac{\text{Gain}}{\text{CP}} \right) \times 100
\]
We will first establish a relationship between the SP and CP of a single article.
Step 3: Detailed Explanation:
Let the Cost Price of one article be \(C\) and the Selling Price of one article be \(S\).
According to the question, the selling price of 20 articles is equal to the cost price of 25 articles. We can write this as:
\[
20 \times S = 25 \times C
\]
Now, let's find the relationship between \(S\) and \(C\) for a single article:
\[
S = \frac{25}{20} C
\]
\[
S = \frac{5}{4} C
\]
This means the selling price is \( \frac{5}{4} \) times the cost price.
The gain (or profit) on one article is the difference between its selling price and cost price:
\[
\text{Gain} = S - C = \frac{5}{4} C - C = \left( \frac{5}{4} - 1 \right) C = \frac{1}{4} C
\]
Now, we can calculate the gain percentage using the formula:
\[
\text{Gain \%} = \left( \frac{\text{Gain}}{C} \right) \times 100 = \left( \frac{\frac{1}{4} C}{C} \right) \times 100
\]
\[
\text{Gain \%} = \frac{1}{4} \times 100 = 25\%
\]
Step 4: Final Answer:
The gain percentage is 25%.