A wholesaler sells a tin of coffee at Rs 528 and faces a loss of 12%. Later he decides to sell the same tin at Rs 636. What will be his profit percentage at this new selling price?

Introduction / Context:
This problem involves two different selling prices for the same product, one at a loss and one at a profit. The wholesaler initially sells at a loss, which allows us to find the cost price. Then, with a higher selling price, we can determine the resulting profit percentage. Questions like this reinforce the method of first finding cost price from one known transaction and then reusing it for another transaction.

Given Data / Assumptions:

• First selling price SP1 = Rs 528 with a 12% loss.
• Second selling price SP2 = Rs 636.
• Let CP be the cost price of the tin.
• We must calculate the profit percentage at SP2.

Concept / Approach:
A loss of 12% means that the selling price is 88% of the cost price. We can use SP1 = 0.88 * CP to find CP. After finding CP, the profit at SP2 is simply SP2 - CP, and the profit percentage is (SP2 - CP) / CP * 100. This two step approach is a standard technique for dealing with changed selling prices in profit and loss questions.

Step-by-Step Solution:
Step 1: Let CP be the cost price.Step 2: At SP1 = 528, loss = 12%, so SP1 = 88% of CP = 0.88 * CP.Step 3: Therefore 0.88 * CP = 528.Step 4: CP = 528 / 0.88 = 600.Step 5: Now consider SP2 = 636.Step 6: Profit at SP2 = 636 - 600 = 36.Step 7: Profit percentage = (36 / 600) * 100 = 6%.Step 8: Therefore the wholesaler makes a 6% profit at the selling price of Rs 636.

Verification / Alternative check:
To check, we verify the initial loss condition. If CP is 600, 12% of 600 is 72, so SP should be 600 - 72 = 528, which matches SP1. For SP2, if CP is 600 and SP is 636, profit is 36. The fraction 36 / 600 reduces to 6 / 100, giving 6%. This confirms that both the loss and profit calculations are correct and consistent with the given data.

Why Other Options Are Wrong:
Option A (7), option B (5) and option D (4) all represent profit percentages that do not match the exact ratio 36 / 600. A 7% profit would require a profit of 42 on a cost of 600, while a 5% profit would need a profit of 30. None of these would lead to a selling price of 636. Only option C, 6, is fully consistent with the numbers given in the question.

Common Pitfalls:
Some students incorrectly take 12% of 528 instead of 12% of cost price when reconstructing CP, which gives a wrong cost price. Others may miscalculate 528 / 0.88. It is important to remember that loss percentage is always on cost price unless explicitly stated otherwise, and that dividing the selling price by (1 - loss rate) is the correct way to find cost price from a loss scenario.

Final Answer:
At the new selling price of Rs 636, the wholesaler makes a 6% profit.