A shopkeeper sells two different articles for Rs. 1000 each. On the first article he makes a profit of 30 percent and on the second article he incurs a loss of 20 percent. What is the net percentage profit or loss over both articles taken together?

Introduction / Context:
This profit and loss question checks how to combine gains and losses over two items when the selling prices are equal. Many learners make the mistake of simply averaging the percentage values, which gives an incorrect result. Instead, we must work with the actual cost prices and selling prices to obtain the true net percentage profit or loss.

Given Data / Assumptions:

• First article is sold for Rs. 1000 with a profit of 30 percent.
• Second article is sold for Rs. 1000 with a loss of 20 percent.
• We assume normal profit and loss definitions based on cost price.
• We need the net percentage profit or loss over both articles together.

Concept / Approach:
The key idea is that percentage profit or loss is always calculated on cost price. When different percentage changes are applied, we must compute the individual cost prices from the given selling prices. Then we add total cost price and total selling price and finally compute the overall percentage change by using the standard formula: percentage profit or loss equals (total selling price minus total cost price) divided by total cost price, multiplied by 100.

Step-by-Step Solution:
Let the selling price of each article be 1000 rupees.For the first article, profit is 30 percent, so cost price one equals 1000 / 1.30 which is approximately 769.23 rupees.For the second article, loss is 20 percent, so 1000 equals 80 percent of cost price two. Therefore, cost price two equals 1000 / 0.80 which is 1250 rupees.Total cost price equals 769.23 plus 1250 which is 2019.23 rupees approximately.Total selling price equals 1000 plus 1000 which is 2000 rupees.Net loss equals total cost price minus total selling price, which is about 19.23 rupees.Percentage loss equals 19.23 / 2019.23 * 100 which is about 0.95 percent.

Verification / Alternative check:
As an approximate check, note that the first article was bought very cheaply compared to 1000 and the second article was bought at a much higher cost. The second cost price is 1250, so the second sale causes a significant rupee loss. When both are added, the total selling price of 2000 is slightly less than the combined cost price of a little over 2019. The difference is clearly very small compared to two thousand, so a loss below one percent is reasonable. This qualitative reasoning supports the detailed calculation that produced a loss close to 0.95 percent.

Why Other Options Are Wrong:
Option 0.85 percent loss is smaller in magnitude than the correct value and does not match the computed ratio of loss to total cost. Option 1.00 percent loss is slightly larger than the correct answer and would require a little more rupee loss than actually occurs here. Option 1.30 percent loss is even larger and clearly exaggerates the loss compared to the actual difference of about 19.23 rupees on a cost of just over two thousand rupees.

Common Pitfalls:
A very common mistake is to average the percentages and say that the shopkeeper has (30 minus 20) divided by 2 equals 5 percent profit, which is completely incorrect. Another mistake is to average directly as (30 minus 20) equals 10 percent profit, ignoring that one percentage is profit and the other is loss. Students also sometimes calculate percentages on the selling price rather than on the cost price, which again leads to wrong results. Always compute exact cost prices for each item and then combine them to find the true overall profit or loss.

Final Answer:
The shopkeeper makes a very small overall loss, and the correct net result is a 0.95 percent loss on the combined transaction.