Question

A cottage industry produces a certain number of pottery articles in a day. It was observed on a particular day 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 Rs.90, find the number of articles produced and the cost each article.

Answer 1

Hint: In the above question we will assume the total number of articles produced be x. Then we will form an equation using the statement given in the question for the cost of production of each article on a particular day. Solve the equation to get the answer.

Complete step-by-step answer: Let the total number articles produced be x.
According to the question, we have
Cost of production of each article on a particular day was 3 more than twice the number of articles produced on that day.
Then the production cost of each article = 3 + 2x
Also the total cost of production on that day was Rs 90.
Total cost of production on that day = x (3 + 2x) = 90
$ \Rightarrow 3x + 2{x^2} = 90$
$ \Rightarrow 2{x^2} + 3x - 90 = 0$
[Solving equation using middle term splitting method]
$ \Rightarrow 2{x^2} + 15x - 12x - 90 = 0$
$ \Rightarrow x(2x + 15) - 6(2x + 15) = 0$
$ \Rightarrow (2x + 15)(x - 6) = 0$
$\therefore x = \dfrac{{ - 15}}{2}$, $6$
Number of articles can never be negative so we do not consider$\dfrac{{ - 15}}{2}$.
Number of articles produced is 6.
Cost of each article = 3 + 2x
                                   = 3 + 2 x 6
                                   = 15 articles
Therefore, the number of articles is 15 and the cost of each article is Rs 6.

Note: In these types of questions, change the given statements into equations, assuming a variable as x or y. In this question we have solved a quadratic equation whose one root is negative and another one is positive. So, we will always consider the positive value or positive root because in this question we want the number of articles and number of articles can never be in a negative number.