Explanation:

- The selling price of the article is Rs600.

- The person made a profit of 50% on the cost price.

- To calculate the cost price, let's denote the cost price as Rs 'x'.

- A 50% profit on the cost price means the selling price is 150% of the cost price.

- Therefore, 150% of x equals Rs600.

- This can be written as:

$$ \frac{150}{100} \times x = 600$$

- Simplifying this, we get:

$$ 1.5x = 600 $$

- Solving for x, we find:

$$ x = \frac{600}{1.5} $$

$$ x = 400 $$

- The cost price of the article is Rs400.

- Option 1: Rs300 - If the cost price was Rs300, a 50% increase would entail a selling price of Rs450, not Rs600.

- Option 2: Rs450 – If the cost price was Rs450, a 50% increase would entail a selling price of Rs675, not Rs600.

- Option 3: Rs400 - A cost price of Rs400 with 50% profit perfectly matches a selling price of Rs600.

- Option 4: Rs350 - If the cost price was Rs350, a 50% increase would entail a selling price of Rs525, not Rs600.