The cost price of 20 articles is the same as the selling price of x articles. If the profit is `25 %,` then the value of x is :

Options

A. 15
B. 16
C. 18
D. 25

Answer

To solve the problem step by step, let's break it down:

### Step 1: Understand the relationship between cost price (CP) and selling price (SP).
Given that the cost price of 20 articles is equal to the selling price of x articles, we can express this relationship mathematically.

Let the cost price of one article be CP.
Then, the cost price of 20 articles = 20 * CP.

Let the selling price of one article be SP.
Then, the selling price of x articles = x * SP.

From the problem, we have:
\[ 20 \times CP = x \times SP \]

### Step 2: Determine the selling price in terms of cost price using profit percentage.
We know that the profit is 25%. This means that the selling price is 125% of the cost price.

In mathematical terms:
\[ SP = CP + 0.25 \times CP = 1.25 \times CP \]

### Step 3: Substitute the selling price in the equation from Step 1.
Now, we can substitute SP in our equation:
\[ 20 \times CP = x \times (1.25 \times CP) \]

### Step 4: Simplify the equation.
We can cancel CP from both sides (assuming CP is not zero):
\[ 20 = x \times 1.25 \]

### Step 5: Solve for x.
To find x, we can rearrange the equation:
\[ x = \frac{20}{1.25} \]

Calculating the right side:
\[ x = 20 \div 1.25 = 16 \]

### Conclusion:
The value of x is 16.

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