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 90, find the number of articles produced and the cost of each article.​

Answer 1

Answer:

1. The number of articles produced on that day = 6 articles
2. The cost of production of each article = Rs 15

Step-by-step explanation:

Given that:

• 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.
• The total cost of production on that day was 90.

To Find:

• The number of articles produced and the cost of each article.

Let us assume:

1. The number of articles produced on that day be x.
2. The cost of production of each article = 2x + 3

We know that:

• Each article costs = Rs (2x + 3)
• x articles cost = Rs (2x + 3)x

Finding the value of x:

According to the question.

x articles cost = Total cost of production

⟶ (2x + 3)x = 90

⟶ 2x² + 3x = 90

⟶ 2x² + 3x - 90

⟶ 2x² + 15x - 12x - 90 = 0

⟶ x(2x + 15) - 6(2x + 15) = 0

⟶ (x - 6) (2x + 15) = 0

⟶ x = 6 or x = - 15/2

• We have to take the value of x equals to 6. Because we have assumed that x is the number of articles which should be a positive number.

Now,

The number of articles produced on that day.

• Number of articles produced = 6 articles

The cost of production of each article.

• Cost of each article = 2x + 3
• Cost of each article = (2 × 6) + 3
• Cost of each article = 12 + 3
• Cost of each article = Rs 15

Answer 2

Answer:

Given :-

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,

To Find :-

number of articles produced and the cost of each article.

Solution :-

Let us assume

Cost of 1 article = (2y + 3)

Cost of total article = (2y + 3)y

Now,

(2y + 3)y = 90

(2y × y) + (3 × y) = 90

2y² + 3y = 90

2y² + 3y - 90 = 0

2y² + (15y - 12y) - 90 = 0

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

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

Either

y = 6

or

y = -15/2

Negative Value can't be accepted

Cost = 2(6) + 3

Cost = ₹15