B

Given information:
- Cost price of 20 articles = Selling price of x articles
- Profit = 25%

Step 1: Understand the concepts
- Cost price: The price at which an article is bought or manufactured.
- Selling price: The price at which an article is sold to the customer.
- Profit: The difference between the selling price and the cost price.

Step 2: Set up the equation
Let's assume the cost price of each article is C and the selling price of each article is S.
According to the given information, the cost price of 20 articles is equal to the selling price of x articles, so we can set up the equation as follows:

20C = xS

Step 3: Calculate the profit
Profit is calculated as the difference between the selling price and the cost price. In this case, the profit is given as 25% of the selling price. So, we can write:

Profit = 0.25S

Step 4: Solve the equation
To find the value of x, we need to eliminate either C or S from the equation. We can do this by dividing both sides of the equation by C:

20 = (xS)/C

Now, we can substitute the value of profit in terms of S:

20 = (xS)/(C + 0.25S)

Step 5: Simplify the equation
To simplify the equation, let's assume the value of C = 1 (we can assume any value for C as it cancels out in the equation).

20 = (xS)/(1 + 0.25S)
20(1 + 0.25S) = xS
20 + 5S = xS
20 = (x - 5)S
20/S = x - 5
x = 20/S + 5

Step 6: Find the value of x
To find the value of x, we need to know the value of S. Since the question does not provide that information, we cannot find the exact value of x. However, we can determine the value of x in terms of S.

Step 7: Determine the value of xa)15b)25c)18d)16
We can substitute different values of S to find the corresponding value of x. Let's try substituting S = 5:

x = 20/5 + 5
x = 4 + 5
x = 9

Therefore, the value of x is 9.

Conclusion:
The correct answer is option D) 16.