At what percentage above the cost price must an article be marked so that, after allowing a customer a discount of 5%, the shopkeeper still makes a profit of 33%?

Introduction / Context:
This question involves finding the required marked price when both profit and discount percentages are given. It is a common type in profit and loss problems where the shopkeeper wants a certain profit even after giving a discount to attract customers. The key idea is to link cost price, marked price and selling price through percentages.

Given Data / Assumptions:
- Let the cost price (CP) of the article be some amount, say 100 units for convenience.
- The shopkeeper wants a profit of 33 percent on the cost price.
- A discount of 5 percent is allowed on the marked price (MP).
- We must find how many percent above CP the article should be marked (that is, MP relative to CP).

Concept / Approach:
The profit percentage is calculated on the cost price, while the discount percentage is calculated on the marked price. The selling price is the link between them. So the steps are: compute the desired selling price using the profit requirement, then relate selling price to marked price using the discount, and finally express marked price as a percentage of cost price. Using CP = 100 makes calculations simpler and more intuitive.

Step-by-Step Solution:
Assume CP = 100. Desired profit = 33% of CP, so desired selling price SP = 100 + 33 = 133. Let the marked price be MP. A 5% discount is allowed, so SP = MP * (1 - 5 / 100) = MP * 0.95. We know SP should be 133, so MP * 0.95 = 133. Therefore, MP = 133 / 0.95. Compute MP = 140. So MP as a percentage of CP is (140 / 100) * 100% = 140% of cost price. Mark up above cost price = 140% - 100% = 40%.

Verification / Alternative check:
Using CP = 100 and the computed MP = 140, let us check: discount 5% on 140 gives SP = 140 * 0.95 = 133. Profit over CP = 133 - 100 = 33, which is 33% of 100. This confirms that our marked price indeed allows a 33 percent profit after giving 5 percent discount.

Why Other Options Are Wrong:
45% and 47%: These would give a marked price higher than needed, and the resulting profit percentage after discount would be more than 33%.
35% and 30%: These mark ups are too low, resulting in a selling price that fails to provide the desired 33% profit on cost price.

Common Pitfalls:
A common mistake is to directly add or subtract percentages without checking which base each percentage refers to. Students may also treat profit and discount as if both directly change cost price, which is incorrect. Always remember that profit is on cost price and discount is on marked price. Using assumed values like CP = 100 makes the relationships clear and prevents arithmetic confusion.

Final Answer:
The article must be marked at 40 percent above its cost price to earn a 33 percent profit after allowing a 5 percent discount.