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 article.

Let there be x articles.
Then the production cost of each article = 3 + 2x
Total production cost = x(3 + 2x) = 90
3x + 2x² = 90
2x² + 3x - 90 = 0
We can solve this quadratic equation using factoring or the quadratic formula. Let's try factoring:
2x² + 15x - 12x - 90 = 0
x(2x + 15) - 6(2x + 15) = 0
(2x + 15)(x - 6) = 0
This gives us two possible solutions for x:
2x + 15 = 0 => x = -15/2
x - 6 = 0 => x = 6
Since the number of articles cannot be negative, we have x = 6.
Therefore, the number of articles produced is 6.
The cost of each article is 3 + 2(6) = 3 + 12 = Rs. 15