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

Let, the number of article = x
Therefore, the cost of one article = 2x + 3
According to question, the total cost = x(2x + 3) = 90
⇒ 2x² +3x = 90
⇒ 2x² + 3x – 90 = 0
⇒ 2x² + 15x – 12x – 90 = 0
⇒ x(2x + 15) – 6 (2x + 15) = 0
⇒ (2x + 15) (x – 6) = 0
⇒ (2x + 15) = 0 or (x – 6) = 0
Either x = – 15/2 or x = 6
But, x ≠ – 15/2, as x is a number of articles.
Therefore, x = 6 and the cost of each articles = 2x + 3 = 2 × 6 + 3 = 15
Hence, the number of articles = 6 and the cost of each article is Rs 15.