The selling price of an article is Rs. 27,692 and at this price the shopkeeper incurs a loss of 14%. If instead the article is sold for Rs. 37,352, what will be the new percentage profit on the transaction?

Introduction / Context:
This question focuses on converting a loss situation into a profit situation by changing the selling price while keeping the cost price constant. Such problems are very common in aptitude tests because they check whether you can correctly move between selling price, cost price, profit percentage, and loss percentage. The key idea is that cost price does not change between the two cases; only the selling price and the corresponding percentage gain or loss change. Once cost price is found from the first scenario, it is reused to compute the profit percentage in the second scenario.

Given Data / Assumptions:
- Initial selling price (SP1) = Rs. 27,692. - At SP1, there is a loss of 14%. - New selling price (SP2) = Rs. 37,352. - Cost price (CP) remains the same in both cases. - We must find the profit percentage when the article is sold at SP2.

Concept / Approach:
The relationship between cost price and selling price under loss is: SP = CP * (1 - loss%). Conversely, under profit we use SP = CP * (1 + profit%). In this problem, the first equation lets us compute CP from SP1 and the 14% loss. Then, using CP along with SP2, we compute the profit percentage using the second formula. The trick is to express percentages as decimals (for example, 14% as 0.14) and work step by step. Using correct formulas and careful arithmetic ensures an accurate profit percentage in the second case.

Step-by-Step Solution:
From the first situation, loss% = 14%, so SP1 = CP * (1 - 0.14) = CP * 0.86. So, CP = SP1 / 0.86 = 27,692 / 0.86. Compute CP: CP = Rs. 32,200. Now consider the second situation with SP2 = Rs. 37,352. Profit = SP2 - CP = 37,352 - 32,200 = Rs. 5,152. Profit percentage = (Profit / CP) * 100. So, Profit% = (5,152 / 32,200) * 100. Compute the ratio: 5,152 / 32,200 = 0.16. Therefore, Profit% = 0.16 * 100 = 16%.

Verification / Alternative check:
Check that CP * 0.86 gives back SP1: 32,200 * 0.86 = 27,692, which matches the given selling price with 14% loss. Check second case: 32,200 * 1.16 = 37,352, which matches SP2 exactly, confirming that a 16% profit is correct. Both checks confirm the internal consistency of the solution.

Why Other Options Are Wrong:
- 13.8% and 14%: These are too close to the original loss percentage and ignore the large increase in selling price. - 18.6%: This would give a selling price greater than Rs. 37,352 for the same cost price. - 12%: This underestimates the profit and conflicts with the computed difference between CP and SP2.

Common Pitfalls:
A frequent mistake is to directly average the 14% loss and some assumed profit percentage without calculating the cost price. Another error is using the formula profit% = (SP2 - SP1) / SP1 * 100, which is wrong because profit is always calculated on cost price, not on previous selling price. Students sometimes forget to convert percentage to decimal correctly, for example using 14 instead of 0.14 in the multiplier.

Final Answer:
When the article is sold for Rs. 37,352, the shopkeeper earns a profit of 16%.