A cottage industry produces a certain number of pottery articles in a day. It was observed on a particular day that the cost of production of each article (in rupees) was 3 more than twice the number of articles produced on that day. If the total cost of production on that day was Rs.90 , find the number of articles produced and the cost of each articles.

Let x be the number of articles produced on that day

Thus cost of production of each article = 2x + 3

Total cost = Rs 90

According to the given condition

x(2x + 3) = 90

⇒ 2x² + 3x - 90 = 0

⇒ 2x² - 12x + 15x – 90 = 0

⇒ 2x(x - 6) + 15(x - 6) = 0

⇒ (2x + 15) (x - 6) = 0

⇒

Since the number of articles produced cannot be negative ∴ x = 6

And the cost of each article = 2 × 6 + 3 = Rs 15

Number of articles = 6

Cost of each article = 15