A vendor buys pens at the rate of 4 for Rs 5 and sells them at the rate of 4 for Rs 3. What is the overall result of this transaction in terms of profit or loss percentage?

Introduction / Context:
This is a classic unit price comparison question. The vendor buys and sells the same item, pens, but at different bulk rates. The aim is to compute the effective cost price and selling price per pen and then determine the gain or loss percentage. Such problems test quick thinking about per unit pricing and profit and loss on that basis.

Given Data / Assumptions:

• Buying rate: 4 pens for Rs 5.
• Selling rate: 4 pens for Rs 3.
• The pens are identical and there are no other costs.
• We need to find overall profit or loss percentage.

Concept / Approach:
To compare profit or loss accurately, we should convert both bulk rates into single unit rates. The cost price per pen is found by dividing the total cost by the number of pens purchased. The selling price per pen is found by dividing the total selling amount by the number of pens sold. Once we have cost price and selling price per unit, we can calculate profit or loss percentage using the standard formula (SP - CP) / CP * 100.

Step-by-Step Solution:
Step 1: Compute cost price per pen. If 4 pens cost Rs 5, then CP per pen = 5 / 4 = Rs 1.25.Step 2: Compute selling price per pen. If 4 pens sell for Rs 3, then SP per pen = 3 / 4 = Rs 0.75.Step 3: Find loss per pen: Loss = CP - SP = 1.25 - 0.75 = Rs 0.50.Step 4: Loss percentage = (Loss / CP) * 100 = (0.50 / 1.25) * 100.Step 5: Simplify 0.50 / 1.25 = 1 / 2.5 = 0.4.Step 6: Therefore loss percentage = 0.4 * 100 = 40%.Step 7: So the vendor suffers a 40 percent loss.

Verification / Alternative check:
We can scale up to a larger common quantity to double check. Suppose the vendor deals with 4 pens. Total cost is Rs 5, total selling revenue is Rs 3. Net loss is Rs 2 on a cost of Rs 5. Loss percentage is (2 / 5) * 100 = 40%, which exactly matches the per pen calculation. This confirms that the earlier steps are correct.

Why Other Options Are Wrong:
Option A (40 percent gain) uses the correct percentage but with the wrong sign; the vendor clearly loses money. Option B (66.6 percent loss) and option C (66.66 percent gain) are both numerically far from the calculated result. Only option D, 40 percent loss, matches the computed loss percentage and correctly identifies the direction of the transaction outcome.

Common Pitfalls:
One common mistake is to compare 5 and 3 directly and incorrectly conclude a different percentage without normalizing to a per unit basis. Another is to mistakenly invert CP and SP when applying the formula, leading to a gain percentage instead of a loss. Careful identification of which value is cost and which is selling price and always computing per unit values help avoid these errors.

Final Answer:
In this transaction the vendor suffers a 40 percent loss.