If selling price of 80 articles is equal to the cost price of 100 articles, then find the gain percentage.

The correct option is 25%.

Let's understand the step-by-step derivation to find the gain percentage:

Let the Cost Price (CP) of 1 article be denoted as x.

Therefore, the Cost Price of 100 articles is equal to:

CP of 100 articles = 100x

According to the given problem statement, the Selling Price (SP) of 80 articles is equal to the Cost Price of 100 articles.

SP of 80 articles = CP of 100 articles = 100x

Now, let's find the Selling Price of 1 article by dividing the total selling price of 80 articles by 80:

SP of 1 article = $\frac{100x}{80}$ = $\frac{5}{4}$x = 1.25x

Since the Selling Price of 1 article (1.25x) is greater than the Cost Price of 1 article (x), there is a gain (profit).

We calculate the gain (profit) on one article as follows:

Gain = SP of 1 article - CP of 1 article
Gain = 1.25x - x = 0.25x

Now, we can find the gain percentage using the formula:

Gain Percentage = $\left(\frac{\text{Gain}}{\text{CP}}\right)\times 100$

Substituting the values of Gain (0.25x) and CP (x) into the formula:

Gain Percentage = $\left(\frac{0.25x}{x}\right)\times 100$
Gain Percentage = 0.25 × 100 = 25%

Thus, the gain percentage is 25%.