A shopkeeper sells two articles for Rs. 1000 each, making a profit of 20% on the first article and a loss of 20% on the second article. What is his overall percentage profit or loss on the two articles taken together?

Introduction / Context:
This question illustrates a common trap in profit and loss: equal percentage profit and loss on equal selling prices does not result in zero net profit. The key issue is that profit and loss percentages are calculated on cost price, not on selling price, so the effective costs differ for the two articles.

Given Data / Assumptions:

• Two articles are sold at Rs. 1000 each.
• On the first article, there is a profit of 20%.
• On the second article, there is a loss of 20%.
• We must find the overall percentage profit or loss on both articles together.

Concept / Approach:
Let cost prices of the first and second articles be C1 and C2. Given the profits and losses, selling price of each is Rs. 1000. For the first, 1000 = 1.20 * C1, and for the second, 1000 = 0.80 * C2. From these equations we compute C1 and C2, find total cost and total selling price, and then determine overall profit or loss percentage as (Total SP - Total CP) / Total CP * 100.

Step-by-Step Solution:
Step 1: For the first article, 1000 = 1.20 * C1, so C1 = 1000 / 1.20 = Rs. 833.33 approximately.Step 2: For the second article, 1000 = 0.80 * C2, so C2 = 1000 / 0.80 = Rs. 1250.Step 3: Total cost price = C1 + C2 = 833.33 + 1250 ≈ Rs. 2083.33.Step 4: Total selling price = 1000 + 1000 = Rs. 2000.Step 5: Overall profit or loss = Total SP - Total CP = 2000 - 2083.33 ≈ -83.33, which is a loss of Rs. 83.33.Step 6: Percentage loss = 83.33 / 2083.33 * 100 ≈ 4%.

Verification / Alternative check:
We can use fractions to be more exact. For the first article, C1 = 1000 / 1.2 = 1000 * 5 / 6 = 833 1/3 rupees.For the second article, C2 = 1000 / 0.8 = 1000 * 5 / 4 = 1250 rupees.Total cost = 2083 1/3 rupees, total SP = 2000 rupees.Loss = 83 1/3 rupees, so loss percentage = (83 1/3) / (2083 1/3) * 100 = 4% exactly.

Why Other Options Are Wrong:
Many people mistakenly choose “No profit no loss” because they see equal and opposite percentages, but that ignores the different bases. A 5% profit or 8% profit would require total SP to exceed total CP, which does not happen here. A 6% loss would imply a larger absolute loss than Rs. 83.33 on this total cost. Only a 4% loss fits the calculations.

Common Pitfalls:
The major pitfall is to assume that a gain of 20% and a loss of 20% simply cancel out. Another error is to average +20% and -20% to get 0%, which is not valid because the percentages apply to different cost prices. Always convert each case to cost price and then compute total profit or loss on the combined cost.

Final Answer:
The shopkeeper incurs an overall 4% loss on the two articles together.