A merchant buys two articles together for Rs 600. He sells one article at a profit of 22% and the other at a loss of 8%, and overall he makes no profit and no loss. What is the selling price of the article that he sells at a loss?

Introduction / Context:
This question is a typical example of mixed transactions where one item is sold at profit and another at loss, but the overall result is break-even. To solve it, we must split the total cost into two unknown cost prices, apply the respective profit and loss percentages, and use the condition that overall profit is zero. From there, we can determine the selling price of the loss-making article.

Given Data / Assumptions:

• Total cost price of two articles = Rs 600.
• First article is sold at a profit of 22%.
• Second article is sold at a loss of 8%.
• Net result: no profit and no loss overall.
• We need the selling price of the article sold at a loss.

Concept / Approach:
Let cost price of the profit article be x and cost price of the loss article be 600 - x. Using the profit and loss percentages, we express both selling prices in terms of x. The condition of no overall profit means total selling price equals total cost price (600). This gives a linear equation in x. Solving for x gives both cost prices, from which we can compute the selling price of the loss article as 92% of its cost price.

Step-by-Step Solution:
Step 1: Let cost of article 1 (profit article) = x.Step 2: Then cost of article 2 (loss article) = 600 - x.Step 3: Selling price of article 1, SP₁ = x * 1.22.Step 4: Selling price of article 2, SP₂ = (600 - x) * 0.92.Step 5: No profit, no loss implies SP₁ + SP₂ = 600.Step 6: So 1.22x + 0.92(600 - x) = 600 ⇒ 1.22x + 552 - 0.92x = 600 ⇒ 0.30x = 48 ⇒ x = 160.Step 7: Then cost of loss article = 600 - 160 = 440, and SP₂ = 0.92 * 440 = 404.8.

Verification / Alternative check:
Check with the computed values: Article 1 has CP = 160 and SP = 160 * 1.22 = 195.2 (profit 35.2). Article 2 has CP = 440 and SP = 404.8 (loss 35.2). Total CP = 600 and total SP = 195.2 + 404.8 = 600. Since the total profit is zero, our solution is consistent and confirms that SP of the loss article is Rs 404.80.

Why Other Options Are Wrong:
Rs 536.80 and Rs 440 do not satisfy the zero net profit condition when used as SP for the loss article. Rs 160 is only the cost price of the profit article, not a selling price at all. Only Rs 404.80 correctly balances the gain on one article with the loss on the other so that the merchant neither gains nor loses overall.

Common Pitfalls:
Students often assume that the two cost prices are equal or that the profit and loss percentages somehow cancel out symmetrically. Others forget to apply percentages to the correct base and mix up profit and loss formulas. Always introduce variables for unknown cost prices, translate the conditions into equations and then solve systematically.

Final Answer:
The selling price of the article sold at a loss is Rs. 404.80.