Ram loses the cost of 6 pens of selling of 144 pens. What is the percentage of loss ?

Options

A. 2
B. 6
C. 14
D. 4

Answer

To find the percentage of loss when Ram sells 144 pens and loses the cost of 6 pens, we can follow these steps:

### Step 1: Define Variables
Let the cost price (CP) of one pen be \( x \). Therefore, the cost price of 144 pens is:
\[ \text{Total CP} = 144x \]
The cost price of 6 pens is:
\[ \text{Cost of 6 pens} = 6x \]

### Step 2: Calculate Selling Price (SP)
According to the problem, Ram loses the cost of 6 pens when selling 144 pens. This means the selling price (SP) of 144 pens is:
\[ \text{Total SP} = \text{Total CP} - \text{Loss} = 144x - 6x = 138x \]

### Step 3: Calculate Loss
The loss incurred is the difference between the total cost price and the total selling price:
\[ \text{Loss} = \text{Total CP} - \text{Total SP} = 144x - 138x = 6x \]

### Step 4: Calculate Percentage of Loss
The percentage of loss can be calculated using the formula:
\[ \text{Percentage of Loss} = \left( \frac{\text{Loss}}{\text{Total CP}} \right) \times 100 \]
Substituting the values we have:
\[ \text{Percentage of Loss} = \left( \frac{6x}{144x} \right) \times 100 \]
Here, \( x \) cancels out:
\[ \text{Percentage of Loss} = \left( \frac{6}{144} \right) \times 100 = \left( \frac{1}{24} \right) \times 100 \]
Calculating this gives:
\[ \text{Percentage of Loss} = \frac{100}{24} \approx 4.17\% \]

### Step 5: Final Answer
Rounding off, the percentage of loss is approximately \( 4\% \).

### Summary
Thus, the percentage of loss when Ram sells 144 pens is \( 4\% \).

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