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 was $Rs90$, find the number of articles produced and the cost of each article.

Answer 1

let us assume the total number of article $=x$

The cost of an article $=2x+3$

Now, we know that

$\begin{array}{rcl}\mathrm{Total}\mathrm{cost}\mathrm{of}\mathrm{production}& =& \mathrm{Cost}\mathrm{of}\mathrm{one}\mathrm{article}\times \mathrm{Number}\mathrm{of}\mathrm{article}\\ 90& =& x\left(2x+3\right)\\ 90& =& 2x^2+3x\\ 2x^2+3x-90& =& 0\\ 2x^2+15x-12x-90& =& 0\\ x\left(2x+15\right)-6\left(2x+15\right)& =& 0\\ \left(2x+15\right)\left(x-6\right)& =& 0\end{array}$

$$\begin{gathered} 2x+15=0andx-6=0 \\ x=\frac{-15}{2}andx=6 \end{gathered}$$

As the articles cannot be in the negative number, hence $x=6$

Therefore, the total number of articles is $6$.

Now, the cost of one article is $2x+3=2\times 6+3=15$

Hence, the cost of one article is $₹15$.