Question

Question 6
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 ₹ 90, find the number of articles produced and the cost of each article.

Answer 1

Let the number of articles produced be $x$.
Therefore, cost of production of each article =$₹(2x+3)$
It is given that the total production is $₹90$.
$\therefore x(2x+3)=90$
$\Rightarrow 2x^2+3x-90=0$
$\Rightarrow 2x^2+15x-12x-90=0$
(Splitting the middle term 3x as 15x-12x because $15x\times -12x=-180x^2$)
$\Rightarrow x(2x+15)-6(2x+15)=0$
$\Rightarrow (2x+15)(x-6)=0$
Either, $2x+15=0orx-6=0$
$\Rightarrow x=-\frac{15}{2}orx=6$
As the number of articles produced can only be a positive integer, so $x$ can only be $6$.
Hence, number of articles produced = $6$
Cost of each article = $2\times 6+3=₹15$Let the number of articles produced be $x$.
Therefore, cost of production of each article =$₹(2x+3)$
It is given that the total production is $₹90$.
$\therefore x(2x+3)=90$
$\Rightarrow 2x^2+3x-90=0$
$\Rightarrow 2x^2+15x-12x-90=0$
(Splitting the middle term 3x as 15x-12x because $15x\times -12x=-180x^2$)
$\Rightarrow x(2x+15)-6(2x+15)=0$
$\Rightarrow (2x+15)(x-6)=0$
Either, $2x+15=0orx-6=0$
$\Rightarrow x=-\frac{15}{2}orx=6$
As the number of articles produced can only be a positive integer, so $x$ can only be $6$.
Hence, number of articles produced = $6$
Cost of each article = $2\times 6+3=₹15$