The cost price of an article is Rs x. The shopkeeper marks it up by 100% and then sells it for Rs 1,200 after allowing a discount of 20% on the marked price. What is the value of x (the cost price in Rs)?

Introduction / Context:
This question combines markup and discount concepts in one transaction. The shopkeeper increases the price by a certain percentage over the cost price (markup), and then offers a discount to sell the item. The final selling price is given, and we are asked to find the original cost price. It is a classic profit and loss problem that requires stepwise reverse calculation.

Given Data / Assumptions:

• Cost price of the article = Rs x.
• Marked price is obtained by marking up the cost price by 100%.
• A discount of 20% is given on this marked price.
• Final selling price after discount = Rs 1,200.

Concept / Approach:
A 100% markup means the marked price is double the cost price. A discount of 20% on the marked price means the selling price is 80% of the marked price. We can express the selling price in terms of x by multiplying the cost price by the markup factor and then by the discount factor. Setting this equal to 1200 and solving for x gives the cost price.

Step-by-Step Solution:
Step 1: Cost price (CP) = Rs x. Step 2: Markup of 100% means marked price (MP) = x + 100% of x = 2x. Step 3: Discount of 20% means selling price (SP) = 80% of MP = 0.80 * MP. Step 4: So SP = 0.80 * 2x = 1.6x. Step 5: Given SP = 1200, so 1.6x = 1200. Step 6: Solve for x: x = 1200 / 1.6. Step 7: Compute x = 750. Step 8: Therefore, the cost price of the article is Rs 750.

Verification / Alternative check:
Use x = 750 to verify. Marked price = 2 * 750 = Rs 1500. Discount = 20% of 1500 = 300. Selling price after discount = 1500 - 300 = Rs 1200, exactly matching the given selling price. This confirms the correctness of the cost price.

Why Other Options Are Wrong:

• 1500: This would be the marked price, not the cost price, given a 100% markup.
• 1000: If x were 1000, marked price would be 2000 and 20% discount gives 1600, not 1200.
• 2000: This cost price is too high and leads to a far larger selling price after discount.
• 600: With this value, marked price becomes 1200 and 20% discount gives 960, which does not match 1200.

Common Pitfalls:
A frequent mistake is to confuse markup with profit and assume that a 100% markup means selling price is simply twice the cost price without considering the discount. Another error is to subtract the discount rate from the markup rate directly, which is not valid because they are applied at different stages. Always express each step with precise multiplication factors to avoid these conceptual traps.

Final Answer:
The cost price of the article is Rs 750.