By selling 168 Pens a shopkeeper gains the of CP of 14 pen. Find his Gain %?

Options

A. `8.33%`
B. `9.375%`
C. `7.14%`
D. `5%`

Answer

To find the gain percentage when a shopkeeper sells 168 pens and gains the cost price of 14 pens, we can follow these steps:

### Step 1: Understand the Given Information
- The number of pens sold = 168
- The gain is equivalent to the cost price of 14 pens.

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

### Step 3: Calculate the Total Cost Price (CP) of 168 Pens
The total cost price (CP) for 168 pens can be calculated as:
\[ \text{Total CP} = 168 \times CP \]

### Step 4: Calculate the Gain
The gain is given as the cost price of 14 pens:
\[ \text{Gain} = 14 \times CP \]

### Step 5: Calculate the Selling Price (SP)
The selling price (SP) for 168 pens can be expressed as:
\[ \text{SP} = \text{Total CP} + \text{Gain} \]
Substituting the values from Steps 3 and 4:
\[ \text{SP} = (168 \times CP) + (14 \times CP) \]
\[ \text{SP} = 182 \times CP \]

### Step 6: Calculate Gain Percentage
The gain percentage can be calculated using the formula:
\[ \text{Gain Percentage} = \left( \frac{\text{Gain}}{\text{Total CP}} \right) \times 100 \]
Substituting the values from Steps 4 and 3:
\[ \text{Gain Percentage} = \left( \frac{14 \times CP}{168 \times CP} \right) \times 100 \]
The CP cancels out:
\[ \text{Gain Percentage} = \left( \frac{14}{168} \right) \times 100 \]

### Step 7: Simplify the Calculation
Now, simplify \( \frac{14}{168} \):
\[ \frac{14}{168} = \frac{1}{12} \]
Now, calculate the gain percentage:
\[ \text{Gain Percentage} = \left( \frac{1}{12} \right) \times 100 = 8.33\% \]

### Final Answer
The gain percentage is **8.33%**.

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