A dealer purchases an article for Rs 900 and fixes the list price so that he can still gain 20% on cost price even after allowing a 10% discount on the list price. What should be the list price of the article?

Introduction / Context:
This question involves determining the list price needed to achieve a desired net profit after giving a discount. The dealer wants a 20% gain on cost price even after allowing a 10% discount on the marked price. Such problems are very common in profit and loss chapters to test multi step reasoning with cost price, marked price, discount and profit percentage.

Given Data / Assumptions:

• Cost price CP = Rs 900.
• Desired profit percentage = 20% on cost.
• Dealer allows a discount of 10% on the list price (marked price).
• We must find the list price (marked price) that satisfies these conditions.

Concept / Approach:
First compute the selling price required to achieve a 20% profit on cost. Then use the given discount percentage to find what the list price must be so that, after discounting, the selling price equals this target value. The relationship between selling price and list price is given by SP = (1 - discount rate) * List price. Rearranging this equation gives the necessary list price once the desired selling price is known.

Step-by-Step Solution:
Step 1: Cost price CP = 900.Step 2: Desired profit = 20% of CP = 0.20 * 900 = 180.Step 3: Required selling price SP = CP + profit = 900 + 180 = Rs 1080.Step 4: The dealer gives a discount of 10% on the list price.Step 5: Let list price be LP. Then SP = LP - 10% of LP = 0.90 * LP.Step 6: Substitute SP = 1080 into 0.90 * LP = 1080.Step 7: LP = 1080 / 0.90 = 1200.Step 8: Therefore the list price must be Rs 1200.

Verification / Alternative check:
We can verify quickly. If LP = 1200, a 10% discount is 120. So SP = 1200 - 120 = 1080. Comparing SP with CP of 900, profit = 1080 - 900 = 180. Profit percentage is 180 / 900 * 100 = 20%, exactly as required. This confirms that the chosen list price produces the correct net profit after discount.

Why Other Options Are Wrong:
Option A (Rs 1180), option B (Rs 1080) and option D (Rs 1100) all give selling prices which either do not match 1080 after a 10% discount or do not yield a 20% profit when compared to CP of 900. Only LP = 1200 gives SP = 1080 and leads to a 20% profit, so option C is the only correct choice.

Common Pitfalls:
Students sometimes mistakenly take 20% profit directly on the list price or subtract both 20% and 10% from the cost price without understanding that profit is computed on CP and discount is computed on list price. Others treat selling price as list price minus 20% instead of 10%. Clearly writing each relation and stating the base of each percentage helps avoid these typical errors.

Final Answer:
The dealer should fix the list price at Rs 1200.