The ratio of cost price to marked price of an article is 2 : 3, and the ratio of percentage profit to percentage discount is 3 : 2. What is the percentage discount allowed on the marked price?

Introduction / Context:
This question belongs to the topic of profit and loss in quantitative aptitude. It combines information about the ratio of cost price to marked price with a ratio between percentage profit and percentage discount. The objective is to determine the discount percentage. Such questions test a learner's ability to translate word statements into algebraic equations and to handle relationships between different commercial terms such as cost price, marked price, selling price, profit and discount.

Given Data / Assumptions:

The ratio of cost price (CP) to marked price (MP) is given as 2 : 3.
The ratio of percentage profit to percentage discount is given as 3 : 2.
Let the percentage profit be represented by p percent and the percentage discount by d percent.
The aim is to find the numerical value of d, the discount percentage, from the options provided.

Concept / Approach:
Key concepts from profit and loss are used. Cost price is the amount paid by the shopkeeper, marked price is the printed price on the article, and selling price is the actual price at which the article is sold. Profit percentage is calculated on cost price, while discount percentage is calculated on marked price. Selling price can be expressed in two ways: one in terms of cost price and profit, and another in terms of marked price and discount. Equating these expressions, and then applying the given ratio between profit percentage and discount percentage, allows us to form an equation in one variable and solve for the discount percentage.

Step-by-Step Solution:
Step 1: Let cost price CP = 2k and marked price MP = 3k, using the ratio 2 : 3. Step 2: Let profit percentage be p percent and discount percentage be d percent. From the ratio of percentages, p : d = 3 : 2, so p = 3x and d = 2x for some positive number x. Step 3: Selling price in terms of cost price and profit is SP = CP * (1 + p/100) = 2k * (1 + 3x/100). Step 4: Selling price in terms of marked price and discount is SP = MP * (1 - d/100) = 3k * (1 - 2x/100). Step 5: Equate the two expressions for SP since both represent the same selling price: 2k * (1 + 3x/100) = 3k * (1 - 2x/100). Step 6: Cancel k from both sides and simplify: 2 * (1 + 3x/100) = 3 * (1 - 2x/100). Step 7: Expand both sides: 2 + 6x/100 = 3 - 6x/100. Step 8: Bring like terms together: 6x/100 + 6x/100 = 3 - 2, which gives 12x/100 = 1. Step 9: Solve for x: x = 100/12 = 25/3. Step 10: Discount percentage d = 2x = 2 * (25/3) = 50/3 percent = 16.66 percent approximately.

Verification / Alternative check:
To verify, use the value d = 16.66 percent and compute back. Then p = 3x = 75/3 = 25 percent. Take CP = 2 and MP = 3 for simplicity. With profit 25 percent on CP, SP in terms of CP is SP = 2 * (1 + 25/100) = 2 * 1.25 = 2.5. With discount 16.66 percent on MP, SP in terms of MP is SP = 3 * (1 - 16.66/100) which is approximately 3 * 0.8334 = 2.5002, very close to 2.5 allowing for rounding. This consistency confirms that the computed discount percentage is correct. Among the given options, 16.66 percent matches this value.

Why Other Options Are Wrong:
20 percent: If discount were 20 percent, the resulting selling price calculated from marked price and cost price would not match simultaneously under the given constraints.
25 percent: This value actually corresponds to the profit percentage in the correct solution, not the discount percentage.
33.33 percent: This discount would be too high relative to the profit, and it would break the required ratio p : d = 3 : 2 and the relationship between cost price and marked price.

Common Pitfalls:
A frequent mistake is confusing the bases on which profit and discount percentages are calculated, that is, treating both on cost price or both on marked price. Another pitfall is misusing the ratio of percentages and directly equating numerical profits and discounts without accounting for their different bases. Some learners also forget to express percentages as fractions over 100 when forming algebraic equations. To avoid these errors, always express selling price in both forms, carefully maintain percentage over 100 in each step, and only then equate the expressions to solve for the unknown.

Final Answer:
The discount allowed on the marked price of the article is approximately 16.66% of the marked price.