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 ₹ 90, find the number of articles produced and the cost of each article.

Let no. of articles produced be x.

So, cost of production of each article = (2x + 3)

Given,

Total cost = 90

⇒ x(2x + 3) = 90

⇒ 2x² + 3x = 90

⇒ 2x² + 3x - 90 = 0

⇒ 2x² + 15x - 12x - 90 = 0

⇒ x(2x + 15) - 6(2x + 15) = 0

⇒ (x - 6)(2x + 15) = 0

⇒ x - 6 = 0 or 2x + 15 = 0

⇒ x = 6 or x = $-\dfrac{15}{2}$.

Since, no. of articles cannot be negative.

∴ x = 6 and 2x + 3 = 2(6) + 3 = 12 + 3 = 15.

Hence, no. of articles produced = 6 and cost of each article = ₹ 15.