The cost price of 20 article is the same as the selling price of x articles. If the profit is 25% find out the value of x

Options

A. 13
B. 14
C. 15
D. 16

Answer

To solve the problem, we need to find the value of \( x \) given that the cost price (CP) of 20 articles is equal to the selling price (SP) of \( x \) articles, and the profit is 25%. Let's break this down step by step.

### Step 1: Define the Cost Price and Selling Price
Let the cost price of one article be \( CP \).

Then, the cost price of 20 articles is:
\[ \text{Cost Price of 20 articles} = 20 \times CP \]

### Step 2: Calculate the Selling Price with Profit
Since the profit is 25%, the selling price of one article can be calculated as:
\[ SP = CP + \text{Profit} \]
The profit is 25% of the cost price, which can be expressed as:
\[ \text{Profit} = 0.25 \times CP \]
Thus, the selling price becomes:
\[ SP = CP + 0.25 \times CP = 1.25 \times CP \]

### Step 3: Express Selling Price of \( x \) Articles
The selling price of \( x \) articles is:
\[ \text{Selling Price of } x \text{ articles} = x \times SP = x \times (1.25 \times CP) = 1.25x \times CP \]

### Step 4: Set Up the Equation
According to the problem, the cost price of 20 articles is equal to the selling price of \( x \) articles:
\[ 20 \times CP = 1.25x \times CP \]

### Step 5: Simplify the Equation
We can cancel \( CP \) from both sides (assuming \( CP \neq 0 \)):
\[ 20 = 1.25x \]

### Step 6: Solve for \( x \)
To find \( x \), we can rearrange the equation:
\[ x = \frac{20}{1.25} \]
Calculating the right side:
\[ x = \frac{20}{1.25} = 16 \]

### Conclusion
Thus, the value of \( x \) is 16.