While selling an article for Rs. 18,450, a person incurs a loss of 50%. At what price should he sell the article to earn a profit of 50% on the same cost price?

Introduction / Context:
This question involves the same article being sold under two different conditions, first at a loss and then at a profit. From the selling price at a 50% loss, we can determine the cost price. Using that same cost price, we then find the selling price required to achieve a 50% profit. This type of question is very common in aptitude tests because it requires you to invert percentage changes and keep track of the base value (cost price) correctly.

Given Data / Assumptions:
- First selling price SP1 = Rs. 18,450. - This first sale involves a 50% loss. - For a 50% loss, SP1 = 50% of cost price. - We need the selling price SP2 that yields a 50% profit on the same cost price.

Concept / Approach:
If a 50% loss occurs, the selling price is half of the cost price. Therefore, SP1 = 0.5 * CP. From this we can find CP by CP = SP1 / 0.5. Once CP is known, a 50% profit means SP2 = 1.5 * CP. The correct approach is to do both steps in order: first find cost price, then find the new selling price for the desired profit percentage. This reinforces the idea that percentage profit or loss is always computed relative to cost price.

Step-by-Step Solution:
Step 1: Let CP be the cost price of the article. Step 2: 50% loss means SP1 = 0.5 * CP. Step 3: Given SP1 = Rs. 18,450, so 0.5 * CP = 18,450. Step 4: Therefore, CP = 18,450 / 0.5 = Rs. 36,900. Step 5: To earn a 50% profit, SP2 must be 1.5 * CP. Step 6: SP2 = 1.5 * 36,900. Step 7: SP2 = 55,350 rupees.

Verification / Alternative check:
We can verify logic by going backwards. If CP is 36,900, then selling at 18,450 is exactly half of the cost price, so loss is 18,450 and loss percentage is 18,450 / 36,900 * 100 = 50%. Selling at 55,350 is 18,450 above 36,900, so profit is 18,450, again equal to 50% of the cost price. This confirms that both the loss and profit percentages are correctly matched to the same cost price.

Why Other Options Are Wrong:
Rs. 52,000, Rs. 56,775, and Rs. 13,837 do not satisfy the condition of a 50% profit when compared with the cost price of 36,900. For example, Rs. 52,000 would give a profit of only 15,100, which is less than half of the cost price. Similarly, Rs. 56,775 would give too large a profit. The unexplained number Rs. 13,837 is far too low even to cover cost price. Only Rs. 55,350 gives exactly a 50% profit.

Common Pitfalls:
One common error is to apply the 50% profit directly to the selling price at loss, rather than to the cost price. Another mistake is to assume that 50% loss and 50% profit cancel out in some way, which is incorrect because they are applied to different bases. Always go through the cost price, since that is the reference for both profit and loss percentages.

Final Answer:
He should sell the article for Rs. 55,350 to earn a 50% profit.