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.
Let the number of article produced on the day be ‘a’.
Given, 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.
Cost of production of each article = 2a + 3
Given, cost of production was Rs. 90
⇒ a(2a + 3) = 90
⇒ 2a2 + 3a – 90 = 0
⇒ 2a – 12a + 15a – 90 = 0
⇒ 2a(a – 6) + 15(a – 6) = 0
⇒ (2a + 15)(a – 6) = 0
⇒ a = 6
Cost of each article = 2 × 6 + 3 = Rs. 15