A store sells boxes of 6 pens for Rs. 30 each and boxes of 12 pens for Rs. 48 each. The price per pen is what per cent less, when purchased in a box of 12 than in a box of 6? 

Options

A. `80%`
B. `75%`
C. `50%`
D. `20%`

Answer

To solve the problem, we need to find the price per pen when purchased in boxes of 6 and 12, and then calculate the percentage difference between the two prices.

### Step 1: Calculate the price per pen in a box of 6
- The cost of a box of 6 pens is Rs. 30.
- To find the price per pen, we divide the total cost by the number of pens:

\[ \text{Price per pen in box of 6} = \frac{30}{6} = 5 \text{ Rs.} \]

### Step 2: Calculate the price per pen in a box of 12
- The cost of a box of 12 pens is Rs. 48.
- To find the price per pen, we divide the total cost by the number of pens:

\[ \text{Price per pen in box of 12} = \frac{48}{12} = 4 \text{ Rs.} \]

### Step 3: Find the difference in price per pen
- Now, we need to find the difference in price per pen between the two boxes:

\[ \text{Difference} = \text{Price per pen in box of 6} - \text{Price per pen in box of 12} = 5 - 4 = 1 \text{ Rs.} \]

### Step 4: Calculate the percentage less
- To find out what percent less the price per pen is when purchased in a box of 12 compared to a box of 6, we use the formula:

\[ \text{Percentage less} = \left( \frac{\text{Difference}}{\text{Price per pen in box of 6}} \right) \times 100 \]

- Substituting the values we have:

\[ \text{Percentage less} = \left( \frac{1}{5} \right) \times 100 = 20\% \]

### Final Answer
The price per pen is 20% less when purchased in a box of 12 than in a box of 6.

---