If the selling price of 10 CDs is the same as the cost price of 12 CDs. What is the profit or loss percent?

Answer

To solve the problem step by step, we can follow these calculations:

### Step 1: Define the Variables
Let the Cost Price (CP) of 1 CD be \( x \). Therefore, the Cost Price of 12 CDs is:
\[ \text{CP of 12 CDs} = 12x \]

### Step 2: Determine the Selling Price
According to the problem, the Selling Price (SP) of 10 CDs is equal to the Cost Price of 12 CDs. Hence, we can write:
\[ \text{SP of 10 CDs} = 12x \]
Let the Selling Price of 1 CD be \( y \). Therefore, the Selling Price of 10 CDs is:
\[ \text{SP of 10 CDs} = 10y \]
Setting these equal gives us:
\[ 10y = 12x \]

### Step 3: Solve for Selling Price per CD
From the equation \( 10y = 12x \), we can solve for \( y \):
\[ y = \frac{12x}{10} = 1.2x \]

### Step 4: Calculate Profit
Now, we can calculate the profit made on each CD:
\[ \text{Profit} = \text{SP} - \text{CP} = y - x = 1.2x - x = 0.2x \]

### Step 5: Calculate Profit Percentage
The profit percentage can be calculated using the formula:
\[ \text{Profit Percentage} = \left( \frac{\text{Profit}}{\text{CP}} \right) \times 100 \]
Substituting the values we have:
\[ \text{Profit Percentage} = \left( \frac{0.2x}{x} \right) \times 100 = 0.2 \times 100 = 20\% \]

### Final Answer
The profit percentage is \( 20\% \).

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