Question

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 is $Rs.90$, find the number of articles and the cost of each article.

Answer 1

Given: Total cost of the production $=Rs.90$

Let the no. of article produced in a particular day be $x.$

Therefore, the cost of production of each article $=Rs.(2x+3)$

The total cost of production $=$ No. of articles $\times$ Cost of each article

$\therefore 90=x(2x+3)$

$\Rightarrow 90=2x^2+3x$

$\Rightarrow 2x^2+3x-90=0$

$\Rightarrow 2x^2+15x-12x-90=0$

$\Rightarrow x(2x+15)-6(x+15)=0$

$\Rightarrow (2x+15)(x-6)=0$

$\Rightarrow (2x+15)=0or,(x-6)=0$

$\therefore x=6$

$x$ cannot be negative, so we will take only positive value.

The no. of articles produced in a day is 6.

and the cost of each article is $(2\times 6+3=Rs.15)$