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

Answer 1

Solution:  Let the number of articles produced in a day = x

             ∴ Cost of production of each article = Z (2x + 3)

             According to the condition,

             Total cost = 90

             ⇒ x × (2x + 3) = 90

             ⇒ 2x² + 3x = 90

             ⇒ 2x² + 3x – 90 = 0

             ⇒ 2x² – 12x + 15x – 90 = 0

             ⇒ 2x(x – 6) + 15(x – 6) = 0

             ⇒ (x – 6) (2x+15) = 0

             ⇒ x – 6 = 0 ⇒ x = 6

             

             But the number of articles cannot be negative.

             

             ⇒ x = 6

             ∴ Cost of each article = Rs (2 × 6 + 3) = Rs. 15

             Thus, the required number of articles produced is 6 and the cost of each article is Rs. 15.