Explanation:

To determine the correct cost price of the article, let's calculate step-by-step:

- Initial Cost Price (CP): Let's say it's Rs. X.

- Marked Price (MP): The dealer marks it 50% above the CP. So, MP = X + 0.5X = 1.5X.

- First Discount: 20% discount reduces the price to 80% of MP. So, after the first discount: 1.5X * 0.8 = 1.2X.

- Second Discount: 15% discount reduces the price further to 85% of the current price. After the second discount: 1.2X * 0.85 = 1.02X.

- Profit: It's given that the dealer gains Rs. 400. Thus, selling price (SP) = CP + Rs. 400. Therefore, 1.02X = X + 400.

Solving 1.02X = X + 400:

- 0.02X = 400

- X = 400 / 0.02

- X = 20,000

- Correct Answer: Option 3, Rs. 20,000.