The profit earned by selling an article for Rs. 832 is equal to the loss incurred by selling the same article for Rs. 448; what should be its selling price to obtain a 50% profit on the cost price?

Introduction / Context:
This profit and loss problem involves an article sold at two different prices, one resulting in a profit and the other in a loss of equal magnitude. Such questions are classic in aptitude exams and help learners understand how to determine the cost price when profit and loss amounts are equal but the selling prices differ. Once cost price is known, we can easily find any required selling price for a desired profit percentage.

Given Data / Assumptions:

• When the article is sold for Rs. 832, there is a profit.
• When it is sold for Rs. 448, there is a loss.
• The profit amount is equal to the loss amount.
• We need to find the selling price that will give a 50% profit.
• Cost price is assumed to be the same in all cases.

Concept / Approach:
Let the cost price be CP and the common magnitude of profit and loss be x. When there is profit, selling price = CP + x. When there is loss, selling price = CP - x. Here, CP + x = 832 and CP - x = 448. Solving these two equations simultaneously will give the values of CP and x. Once CP is known, a 50% profit corresponds to a selling price of 1.5 times CP. This stepwise algebraic method is clean and commonly used.

Step-by-Step Solution:
Step 1: Let the cost price of the article be CP.Step 2: Let the profit (or loss) amount be x.Step 3: From selling at a profit, CP + x = 832.Step 4: From selling at a loss, CP - x = 448.Step 5: Add these two equations: (CP + x) + (CP - x) = 832 + 448.Step 6: This simplifies to 2CP = 1280.Step 7: Hence CP = 1280 / 2 = Rs. 640.Step 8: Now we need a 50% profit on CP.Step 9: 50% of CP = 0.5 * 640 = Rs. 320.Step 10: Required selling price = CP + 50% of CP = 640 + 320 = Rs. 960.

Verification / Alternative check:
We can confirm the consistency of CP = 640 with the original data. Profit at selling price 832 is 832 - 640 = Rs. 192. Loss at selling price 448 is 640 - 448 = Rs. 192. Since profit and loss amounts match, CP = 640 is correct. Then for 50% profit, selling price must be 1.5 * 640 = Rs. 960. The result aligns perfectly with the required condition, so there is no contradiction.

Why Other Options Are Wrong:

• Rs. 660 and Rs. 560: These values are much closer to the lower selling price and do not represent a 50% gain over CP.
• Rs. 1060: This would be far more than a 50% profit. If CP is 640, then 1060 corresponds to a profit of 420, which is 65.625%.

Common Pitfalls:

• Assuming that the average of the two selling prices is the cost price without proper reasoning. In this case that average indeed equals CP only because the profit and loss are equal, but the reasoning should involve algebra.
• Confusing percentage profit with absolute profit amount.
• Incorrectly computing 50% of cost price or adding it to CP.

Final Answer:
The article should be sold for Rs. 960 to earn a 50% profit on the cost price.