To solve this problem, we need to determine the profit percentage when the retail seller buys 30 pencils at the marked price of 27 pens.

Step 1: Understand the Problem

• The seller buys 30 pencils, but instead of paying the price for 30 pencils, they pay the price for 27 pens.
• We need to determine the profit percentage.

Step 2: Assume Prices

Let:

• The marked price of one pencil = $P$ units (currency)
• The marked price of one pen = $Q$ units (currency)

Step 3: Calculate Cost Price

• The cost price of 30 pencils = $30 \times P$
• The amount paid by the seller = $27 \times Q$

Step 4: Express Profit

Profit is calculated as the difference between the selling price and the cost price.

However, the problem states the seller buys at the cost of 27 pens instead of 30 pencils. So the profit can be seen as the difference between what they would have paid (30 pencils) and what they actually paid (27 pens).

Profit = (Cost of 30 pencils) - (Cost paid for 27 pens)
Profit = $30P - 27Q$

Step 5: Calculate the Profit Percentage

Profit percentage is calculated using the formula:

$\text{Profit Percentage} = \left(\frac{\text{Profit}}{\text{Cost Price}}\right) \times 100$

Since the cost price for the seller is $27Q$ (what they actually paid),

$\text{Profit Percentage} = \left(\frac{30P - 27Q}{27Q}\right) \times 100$

Step 6: Simplify the Expression

This expression depends on the relationship between the prices $P$ and $Q$. Without the exact values of $P$ and $Q$, we cannot simplify further. However, this formula will give the profit percentage once $P$ and $Q$ are known.

Conclusion:

To find the exact profit percentage, you'd need the specific prices of the pencil and pen. But the general formula is:

$\text{Profit Percentage} = \left(\frac{30P - 27Q}{27Q}\right) \times 100$

Would you like to see the calculations with specific values, or do you have any further questions on this? Here are some related questions you might find interesting:

1. If the price of a pencil is half that of a pen, what is the profit percentage?
2. How would the profit percentage change if the seller bought 50 pencils at the price of 45 pens?
3. What would be the profit percentage if the seller bought the pencils at a discount?
4. How does the profit percentage change if the number of pencils purchased increases?
5. What happens to the profit percentage if the price of the pen is increased?

Tip: Always ensure you understand the relationship between different products' prices when dealing with percentage profit or loss.