If the cost price of 16 pens is equal to the selling price of 12 pens,then the gain or loss percent is

Options

A. `33(1)/(3)%` gain
B. `25%` gain
C. `25%` loss
D. `33(1)/(3)` loss

Answer

To solve the problem, we will follow these steps:

### Step 1: Define the Cost Price (CP) of One Pen
Let the cost price of one pen be \( X \).

### Step 2: Calculate the Total Cost Price for 16 Pens
The cost price of 16 pens will be:
\[ \text{CP of 16 pens} = 16X \]

### Step 3: Calculate the Selling Price (SP) of 12 Pens
According to the problem, the cost price of 16 pens is equal to the selling price of 12 pens. Therefore:
\[ \text{SP of 12 pens} = 16X \]

### Step 4: Calculate the Cost Price for 12 Pens
The cost price of 12 pens will be:
\[ \text{CP of 12 pens} = 12X \]

### Step 5: Calculate the Gain
The gain can be calculated as:
\[ \text{Gain} = \text{SP} - \text{CP} = 16X - 12X = 4X \]

### Step 6: Calculate the Gain Percentage
The gain percentage is calculated using the formula:
\[ \text{Gain Percentage} = \left( \frac{\text{Gain}}{\text{CP}} \right) \times 100 \]
Substituting the values we have:
\[ \text{Gain Percentage} = \left( \frac{4X}{12X} \right) \times 100 \]

### Step 7: Simplify the Gain Percentage
Simplifying the expression:
\[ \text{Gain Percentage} = \left( \frac{4}{12} \right) \times 100 = \left( \frac{1}{3} \right) \times 100 = 33.33\% \]

### Conclusion
Thus, the gain percentage is \( 33.33\% \).

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