A cottage industry produces a certain number of pottery articles in a day.

Solution:

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 $=15$.