Raju sells an article at a discount of 8% for Rs 17,940 and still makes a profit of 19.6% on the cost price. If he sells the article without offering any discount, what profit percentage would he earn?

Introduction / Context:
This problem checks your understanding of how discount, marked price, cost price and profit percentage are related. Raju sells an article with a discount and still earns profit. We must reverse engineer the cost price and then see what happens if the discount is removed. Such questions are very common in aptitude tests and require systematic use of percentage formulas.

Given Data / Assumptions:

• Selling price with discount (SP₁) = Rs 17,940.
• Discount allowed = 8% on marked price.
• Profit at this selling price = 19.6% on cost price.
• If no discount is given, selling price becomes equal to the marked price (MP).
• We need the new profit percentage without discount.

Concept / Approach:
First, use the profit information at SP₁ to find the cost price. Then, use the discount relation to find the marked price. When the discount is removed, the new selling price equals MP. Finally, compute the profit percentage using the formula profit% = (SP - CP) / CP * 100. Doing the steps in this order prevents mixing up MP, CP and SP.

Step-by-Step Solution:
Step 1: Let cost price = CP. Given profit at SP₁ is 19.6%, so SP₁ = 1.196 * CP.Step 2: 17,940 = 1.196 * CP ⇒ CP = 17,940 / 1.196 = 15,000.Step 3: 8% discount means SP₁ = 92% of MP. So 17,940 = 0.92 * MP ⇒ MP = 17,940 / 0.92 = 19,500.Step 4: Without discount, new SP = MP = Rs 19,500.Step 5: Profit in this case = 19,500 - 15,000 = 4,500, so profit% = (4,500 / 15,000) * 100 = 30%.

Verification / Alternative check:
You can double check by recomputing with the obtained values. At CP = 15,000 and SP₁ = 17,940, profit = 2,940 which is indeed 19.6% of 15,000. At SP = 19,500, the profit of 4,500 over 15,000 clearly gives 30%. This confirms that no arithmetic error has occurred in the percentage calculations.

Why Other Options Are Wrong:
27%, 32% and 25% come from typical mistakes such as using the discount percent on cost price instead of marked price, or mixing up 1.196 and 0.196 while forming equations. They do not satisfy both conditions of the problem simultaneously. Only 30% fits the conditions of both the given discount case and the no-discount case.

Common Pitfalls:
Students often try to jump directly from the discounted selling price to the new profit percentage without first finding the cost price and marked price separately. Another mistake is to treat the 8% discount as applied to cost price, which is incorrect. Always remember that discount is calculated on the marked price and profit or loss is calculated on the cost price unless specifically stated otherwise.

Final Answer:
If Raju sells without any discount, his profit percentage becomes 30%.