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.
Solution:
Let x be the number of articles produced.
Therefore, cost of production of each article = Rs (2x + 3)
Given the total cost of production is Rs. 90
∴ x(2x + 3) = 90
⇒ 2x2 + 3x – 90 = 0
⇒ 2x2 + 15x -12x – 90 = 0
⇒ x(2x + 15) -6(2x + 15) = 0
⇒ (2x + 15)(x – 6) = 0
Thus, either 2x + 15 = 0 or x – 6 = 0
⇒ x = -15/2 or x = 6
As the number of articles produced can only be a positive integer, x can only be 6.
Hence, the number of articles produced = 6
Cost of each article = 2 × 6 + 3 = Rs. 15