A dealer sells an article at a discount of 5 percent on the marked price. The marked price is 12 percent above the cost price, and the article is sold for 532 rupees. What is the cost price of the article?

Introduction / Context:
This problem links cost price, marked price, discount percentage, and final selling price. It is a typical profit and loss question where you must move backward from selling price through discount and marked price to find the cost price. Understanding these chained relationships is essential for exam problems about pricing.

Given Data / Assumptions:
- Let cost price (CP) be C rupees.
- Marked price (MP) is 12 percent above CP, so MP = C * (1 + 0.12) = 1.12 * C.
- Discount given = 5 percent on MP.
- So selling price (SP) is 95 percent of MP, that is 0.95 * MP.
- The actual selling price is given as 532 rupees.
- We must find the cost price C.

Concept / Approach:
The marked price is a fixed percentage above cost price, and discount is a percentage of the marked price. We express SP in terms of CP using both relationships and then set it equal to the given selling price. This produces a direct equation in C. Solving that equation yields the cost price.

Step-by-Step Solution:
Step 1: Marked price MP = 1.12 * C.Step 2: A 5 percent discount on MP means the customer pays 95 percent of MP.Step 3: Therefore, selling price SP = 0.95 * MP = 0.95 * 1.12 * C.Step 4: Multiply 0.95 and 1.12: 0.95 * 1.12 = 1.064.Step 5: So SP = 1.064 * C.Step 6: Given SP = 532 rupees, we have 1.064 * C = 532.Step 7: Solve for C: C = 532 / 1.064.Step 8: Compute 532 / 1.064 = 500 rupees.

Verification / Alternative check:
Check by moving forward. If CP = 500 rupees, then MP = 1.12 * 500 = 560 rupees. A 5 percent discount on 560 rupees is 0.05 * 560 = 28 rupees. So SP = 560 - 28 = 532 rupees, matching the given selling price. This confirms that cost price equals 500 rupees.

Why Other Options Are Wrong:
- 525, 505, and 520 rupees do not produce a marked price and discounted selling price that equal 532 when the same percentage relationships are applied.

Common Pitfalls:
Some students mistakenly apply 12 percent on the selling price instead of on the cost price, or treat the 5 percent discount as applied on cost price instead of on marked price. Another common error is to add the percentages directly without considering that one is a markup and the other a discount. Always write an explicit expression for SP in terms of CP and then solve systematically.

Final Answer:
The cost price of the article is 500 rupees.