(Q8) 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 Rs.90,find the number of articles produced and the cost of each article.

Answer

Let the number of articles produced be x.

Then the cost of each article = 2x + 3

Total cost of the articles produced = x[2x + 3] = 2x2 + 3x

By problem 2x2 + 3x = 90

2x2 + 3x - 90 = 0

2x2 + 15x - x - 90 = 0

x(2x + 15) - (2x + 15) = 0

(2x + 15)(x - ) = 0

2x + 15 = 0 (or) x - = 0 x =
- 15
2
 or x =
But x cant be negative.
∴x =
2x + 3 = 2× + 3 = 15

∴ Number of articles produced = cost of each article = Rs..