The cost of 25 itmes is the same as the revenue earned by selling x items. Find x, if the profit made in the transaction is 25%

Options

A. 0.25
B. 0.1667
C. 0.2
D. 32

Answer

To find the value of \( x \), we can follow these steps:

### Step 1: Understand the given information
We know that the cost of 25 items is the same as the revenue earned by selling \( x \) items, and the profit made in the transaction is 25%.

### Step 2: Define the Cost Price (CP)
Let the cost price of one item be \( CP \). Therefore, the total cost price for 25 items is:
\[ \text{Total CP} = 25 \times CP \]

### Step 3: Define the Selling Price (SP)
Since the profit is 25%, the selling price (SP) can be calculated as:
\[ SP = CP + \text{Profit} \]
The profit is 25% of the cost price, which can be expressed as:
\[ \text{Profit} = 0.25 \times \text{Total CP} = 0.25 \times (25 \times CP) = 6.25 \times CP \]
Thus, the selling price for 25 items is:
\[ SP = 25 \times CP + 6.25 \times CP = 31.25 \times CP \]

### Step 4: Relate Selling Price to Revenue
The revenue earned by selling \( x \) items is equal to the selling price of those \( x \) items:
\[ \text{Revenue} = x \times SP_{\text{per item}} = x \times (CP + 0.25 \times CP) = x \times 1.25 \times CP \]

### Step 5: Set up the equation
Since the total revenue from selling \( x \) items is equal to the total cost of 25 items, we can set up the equation:
\[ x \times 1.25 \times CP = 25 \times CP \]

### Step 6: Cancel out CP
Assuming \( CP \neq 0 \), we can divide both sides by \( CP \):
\[ x \times 1.25 = 25 \]

### Step 7: Solve for \( x \)
Now, we can solve for \( x \):
\[ x = \frac{25}{1.25} = 20 \]

### Conclusion
The value of \( x \) is \( 20 \).

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