The cost price of an article is x rupees. It is marked up by 150 percent, and then sold for Rs 600 after giving a 40 percent discount on the marked price. What is the value of x (the cost price)?

Introduction / Context:
This profit and loss question combines percentage markup with percentage discount. The article is first marked up by a certain percentage over cost price and then sold after applying a discount. We are given the final selling price and must work back to find the original cost price. Such layered percentage problems are standard in competitive exams.

Given Data / Assumptions:
Cost price = x rupees. Markup rate on cost price = 150 percent. Discount on marked price = 40 percent. Final selling price after discount = Rs 600. We must find x, the cost price.

Concept / Approach:
Markup of 150 percent means the marked price is cost price multiplied by 1 plus 1.5, that is 2.5 times the cost price. A discount of 40 percent means the selling price is 60 percent of the marked price. Therefore, selling price becomes 2.5 * x * 0.6. Setting this equal to 600 allows us to solve for x directly.

Step-by-Step Solution:
Marked price M = x * (1 + 150/100) = x * 2.5. Discount rate = 40 percent, so selling price S = M * (1 - 40/100) = M * 0.6. Substitute M: S = 2.5x * 0.6. Compute 2.5 * 0.6 = 1.5, so S = 1.5x. We are given S = 600, so 1.5x = 600. Therefore x = 600 / 1.5. Compute 600 / 1.5 = 400. Thus the cost price is Rs 400.

Verification / Alternative check:
Start with cost price Rs 400. Markup 150 percent means marked price M = 400 + 150 percent of 400 = 400 + 600 = 1000, or directly 2.5 * 400 = 1000. Discount of 40 percent on 1000 gives selling price S = 60 percent of 1000 = 600. This matches the given selling price, confirming that cost price is 400.

Why Other Options Are Wrong:
If cost price were 300, selling price would be 2.5 * 300 * 0.6 = 450, not 600. For 500, selling price would be 2.5 * 500 * 0.6 = 750. For 444 or 666 the computed selling prices do not equal 600 when the same percentage steps are applied. Only 400 satisfies the given final selling price exactly.

Common Pitfalls:
A common mistake is to subtract 150 and 40 directly or to treat discount and markup on the same base value. Another frequent error is to apply 40 percent discount on cost price instead of on marked price. Clearly identifying which percentage acts on which base is crucial for solving such problems correctly.

Final Answer:
The value of the cost price x is Rs 400.