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 on 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 the number of article produced by the cottage industry be $x$.
Then the cost of production of each article $=$ Rs. $(2 x+3)$
It is given that total cost of production =Rs. 90
Therefore,
$x(2 x+3)=90$
$2 x^{2}+3 x=90$
$2 x^{2}+3 x-90=0$
$2 x^{2}-12 x+15 x-90=0$
$2 x(x-6)+15(x-6)=0$
$(x-6)(2 x+15)=0$
Therefore, x cannot be negative.
So, when $x=6$ then
$(2 x+3)=(2 \times 6+3)$
$=12+3$
$=15$
Hence, the number of article produced by the cottage industry be $x=6$ and the cost of production of each article $=15$.