The cost price of an article is x rupees.\nIt is marked up by 120% above cost and then sold after giving a 20% discount on the marked price.\nIf the final selling price is Rs. 8800, what is the value of x?

Introduction / Context:
This question connects cost price, marked price, discount, and selling price. It is a typical profit and loss problem where multiple percentage changes occur in sequence. Being able to translate such a description into a clear algebraic expression is important for many competitive examinations and practical business calculations.

Given Data / Assumptions:

• Cost price (CP) of the article = x rupees.
• The article is marked up by 120% above CP.
• A 20% discount is then given on the marked price.
• The final selling price (SP) after discount = Rs. 8800.
• We need to find the cost price x.

Concept / Approach:
First, we convert the markup into a multiplier for the cost price. A markup of 120% means the marked price is equal to CP plus 120% of CP, which is 2.2 times CP. Next, a 20% discount on the marked price leaves 80% of that marked price as the selling price. Thus, SP = marked price * 0.8 = 2.2 * CP * 0.8. With SP given as 8800, we can solve for CP using a simple algebraic equation. This chain of multiplicative factors is the key idea.

Step-by-Step Solution:
Step 1: Marked price (MP) after 120% markup on cost price x: MP = x + 1.2 * x = 2.2 * x.Step 2: Discount of 20% on MP means the selling price SP = MP * (1 - 20/100) = MP * 0.8.Step 3: Substitute MP: SP = 2.2 * x * 0.8 = 1.76 * x.Step 4: We are told SP = Rs. 8800, so 1.76 * x = 8800.Step 5: Solve for x: x = 8800 / 1.76.Step 6: Compute the value: 8800 / 1.76 = 5000, so the cost price x is Rs. 5000.

Verification / Alternative check:
Verify by reconstructing the entire process from CP = Rs. 5000. Marked price = 2.2 * 5000 = Rs. 11,000. A 20% discount on 11,000 is 11,000 * 20 / 100 = 2200, so the selling price is 11,000 - 2200 = 8800 rupees. This matches the given selling price in the question, confirming that our cost price is correct.

Why Other Options Are Wrong:
If x = 7680, then MP would be 2.2 * 7680, and after 20% discount the selling price would be different from 8800.
Similarly, x = 6000 or x = 6680 would lead to selling prices that do not equal 8800 when the markup and discount are applied.
4400 as cost price also fails to produce 8800 rupees under the given percentage operations.

Common Pitfalls:
A frequent mistake is to treat the markup and discount as additive instead of multiplicative effects or to apply the 20% discount on cost price instead of the marked price. Another common error is to misunderstand the 120% markup as making the marked price 120% of cost price instead of 220% of cost price. To avoid such issues, always express markups and discounts as clear multipliers relative to the appropriate base value, and then chain them carefully in the correct order.

Final Answer:
The cost price x of the article is Rs. 5000.