Final answer:
The market price of the article is `600.
Step-by-step explanation:
To determine the market price, we need to find the original price of the article before the discount. Let's assume the market price is 'M'.
Given that the shopkeeper gives a discount of 10% and still gains 20%, we can set up the following equation:
- The shopkeeper sells the article at 90% of the market price (0.9M) to the customer.
- The shopkeeper gains 20%, which means the selling price is 120% (1.2) of the cost price.
- Using the given cost price of `450, we can set up the equation: 1.2 * 450 = 0.9M
- Solving for M, we find that the market price of the article is `600.
Therefore, the market price for the article is `600.