A shopkeeper sells two articles at Rs. 1000 each. On the first article he makes a profit of 20 percent, while on the second article he incurs a loss of 20 percent. What is his overall net result as a percentage, and is it a profit or a loss?

Introduction / Context:
This is a well known profit and loss pattern where equal percentage gain and loss on equal selling prices or equal cost prices may lead to an overall loss. The main goal is to combine a 20 percent profit and a 20 percent loss on two different transactions of equal selling price and see whether the net result is profit or loss, and by what percentage.

Given Data / Assumptions:

• First article selling price is Rs. 1000 with 20 percent profit.
• Second article selling price is Rs. 1000 with 20 percent loss.
• Both articles are independent transactions.
• We must compute the overall percentage profit or loss on the combined cost price.
• Standard profit and loss definitions apply.

Concept / Approach:
As profit and loss percentages are always calculated on cost price, we first find the cost price of each article from its selling price and percentage profit or loss. Then we add both cost prices to obtain the total cost, and add both selling prices to obtain total revenue. The net difference tells us the overall profit or loss. Finally, we compute the net percentage with respect to the total cost price.

Step-by-Step Solution:
For the first article, selling price S1 equals 1000 rupees and profit is 20 percent.Cost price C1 equals S1 divided by 1.20 which is 1000 / 1.20 equals approximately 833.33 rupees.For the second article, selling price S2 equals 1000 rupees and loss is 20 percent.Selling price in this case is 80 percent of cost, so cost price C2 equals 1000 / 0.80 equals 1250 rupees.Total cost price equals C1 plus C2 which is about 833.33 plus 1250 equals 2083.33 rupees.Total selling price equals S1 plus S2 which is 1000 plus 1000 equals 2000 rupees.Net loss equals total cost price minus total selling price which is 2083.33 minus 2000 equals 83.33 rupees approximately.Percentage loss equals 83.33 divided by 2083.33 multiplied by 100, which is exactly 4 percent.

Verification / Alternative check:
This scenario is a standard result: a 20 percent gain and a 20 percent loss on equal amounts does not cancel out but results in a net loss. Algebraically, if cost price is 100, a 20 percent profit gives selling price 120, while a 20 percent loss gives selling price 80. The total cost would be 100 plus 100 equals 200 and total selling price would be 120 plus 80 equals 200. That example shows no net profit or loss when the cost prices are equal. However, in this question, the selling prices are equal instead. Equal selling prices with equal percentage gain and loss always lead to a net loss, which can be verified by the detailed numerical calculation shown above.

Why Other Options Are Wrong:
A 2 percent loss or 3 percent loss would require a smaller difference between total cost and total selling price than the one we computed. A 2.5 percent loss lies between these but also does not match the exact ratio of 83.33 to 2083.33. Only a 4 percent loss aligns with the actual numbers derived from the given percentages and selling prices.

Common Pitfalls:
Many learners erroneously think that a 20 percent profit and a 20 percent loss should cancel out and give no overall change. This is false because the base amounts for profit and loss are different for each article, due to different cost prices. Another pitfall is to average the two percentages directly, giving zero, which once again ignores that percentage calculations are always on cost price, not on selling price. Carefully computing cost prices first avoids such mistakes.

Final Answer:
The shopkeeper suffers an overall 4 percent loss on the two articles together.