By selling 1 dozen ball pens, a shopkeeper earned the profit equal to the selling price of 4 ball pens. His profit per cent is

Options

A. 0.5
B. 0.4
C. 33 `1/3` %
D. 31 `1/4` %

Answer

To find the profit percentage, we can follow these steps:

### Step 1: Understand the problem
The problem states that by selling 1 dozen (12) ball pens, the shopkeeper earns a profit equal to the selling price of 4 ball pens.

### Step 2: Define the variables
Let:
- SP = Selling Price of 1 ball pen
- CP = Cost Price of 1 ball pen

### Step 3: Write the equation for profit
According to the problem, the profit earned by selling 1 dozen ball pens is equal to the selling price of 4 ball pens. Therefore, we can express this as:
\[ \text{Profit} = \text{Selling Price of 12 ball pens} - \text{Cost Price of 12 ball pens} \]
\[ \text{Profit} = 12 \times SP - 12 \times CP \]
And we know that:
\[ \text{Profit} = 4 \times SP \]

### Step 4: Set up the equation
From the above two equations, we can set up the following equation:
\[ 12 \times SP - 12 \times CP = 4 \times SP \]

### Step 5: Rearrange the equation
Rearranging the equation gives:
\[ 12 \times SP - 4 \times SP = 12 \times CP \]
\[ 8 \times SP = 12 \times CP \]

### Step 6: Find the ratio of SP to CP
Dividing both sides by 4:
\[ 2 \times SP = 3 \times CP \]
Now, we can express the ratio of SP to CP:
\[ \frac{SP}{CP} = \frac{3}{2} \]

### Step 7: Calculate the profit percentage
The profit percentage can be calculated using the formula:
\[ \text{Profit Percentage} = \left( \frac{\text{SP} - \text{CP}}{\text{CP}} \right) \times 100 \]
From the ratio we found:
- SP = 3 units
- CP = 2 units

So, the profit is:
\[ \text{Profit} = SP - CP = 3 - 2 = 1 \]

Now substituting into the profit percentage formula:
\[ \text{Profit Percentage} = \left( \frac{1}{2} \right) \times 100 = 50\% \]

### Final Answer
The profit percentage is **50%**.

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