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

Answer:

Given: The total cost of production= Rs.90

Let the number of pottery articles produced be x.

Therefore, cost of production of each article = Rs (2x + 3)      

the total cost of production = no. of  pottery articles produced × cost of production

A.T.Q

90.= x(2x + 3) = 0

⇒ 2x²+ 3x – 90 = 0

⇒ 2x² + 15x -12x – 90 = 0

⇒ x(2x + 15) -6(2x + 15) = 0

⇒ (2x + 15)(x – 6) = 0

Now 2x+15=0 ⇒2x= - 15

⇒x= -15/2

 ⇒x – 6 = 0

⇒x=6

⇒ x = -15/2 or x = 6

As the number of articles produced can only be a positive integer, therefore, x can only be 6.

Hence, number of articles produced = 6

Hence, number of articles produced = 6Cost of each article = 2 × 6 + 3 = Rs 15.

Answer 2

$\sf\large{\underline{\underline{Solution:}}}$

✏Let the number of articles produced in a day be "x" and the cost of Production of each articles be Rs. Y.

✏Then according to the question,

we have:y = 3 + 2x .......(i)

$\sf\large{\underline{\underline{Also,}}}$

• ✏given that the total cost of production is Rs. 90

$\sf\large{\underline{\underline{Therefore,}}}$

xy = 90

$\sf\large{ x(3 + 2x) = 90{ [From (i)]}}$

=》 2x sq. + 3x - 90 = 0

=》 2x sq. + 15x - 12x - 90= 0

=》 x(2x + 15) - 6(2x + 15) = 0

=》 (x - 6) (2x + 15) = 0

=》 x = 6 or x = -15/2

✏Since the number of articles produced cannot be negative,so x = -15/2 is rejected.

•°• Number of articles = 6and cost of each article = Rs. (3 + 2 × 6)= Rs. 15✔

Hence, cost of each article is Rs. 15✍