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

Let the number of pottery articles be ‘x’. 

Cost of production of each (in rupees) is = (2x + 3) 

∴ 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 

If x – 6 = 0, then x = 6 

If 2x + 15 = 0, then 2x = -15 

∴ x = \(\frac{-15}{2}\)

∴ Number of pottery articles produced is 6. 

Cost of production of 6 pottery articles is Rs. 90 

Cost of production of 1 pottery article ……….. ? 

\(\frac{1\times 90}{6}\) = Rs. 15 

OR Cost of Production= 2x + 3 

= 2 × 6 + 3 

= 12 + 3 

= Rs. 15.