Question

5 À cottage industry produces a certain number
of pottery articles in a day. It was observed
on a patticular day that the cost
production of each article was
3 more than
twice the number of articles prodored on
that day. If the total cost of production
on that day was Rs.90, find the
the cost of
of articles produced and
each article.
nomber​

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

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

Hope it helps..........................................

Answer 2

Answer:

this is the answer

no.of articles = 6

cost of each article= 90÷6= ₹15

and

the total cost of production= 90

Explanation:

let the cost of production of each article be x and the total no. of articles be y

Now,

case I

1. cost of production of each article= 3+ 2*(total no. of articles produced that day)
2. $x = 3 + 2y$

case II

1. cost of production= total no. of articles * cost of each article
2. $xy = 90$
3. $x = \frac{90}{y}$

Now,

from case I (2)

$x = 3 + 2y \\ using \: case \: 2\: (3) \\ \frac{90}{y} = 3 + 2y \\ 90 = y(3 + 2y) \\ 90 = 2{y}^{2} + 3y \\ 2 {y}^{2} + 3y - 90 = 0 \\ 2 {y}^{2} + 15y - 12y - 90 = 0 \\ y(2y + 15) - 6(2y + 15) = 0 \\ (2y + 15)(y - 6) = 0$

$(2y + 15)(y - 6) = 0$

Now,

$since \: \\ (2y + 15) = 0 \\ y = \frac{ - 15}{2} \\ and \: \\ (y - 6) = 0 \\ y = 6$

since value of articles produced can not be negative

therefore,

$y = 6$

now,

According to the question

no.of articles = 6

cost of each article= 90÷6= ₹15

and

the total cost of production= 90

HOPE IT HELPS