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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. - CBSE Class 10 - Mathematics

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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.

Solution

Let the number of articles produced be x.

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

It is given that the total production is Rs 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

Either 2x + 15 = 0 or x - 6 = 0

⇒ 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.

  Is there an error in this question or solution?

APPEARS IN

 NCERT Solution for Mathematics Textbook for Class 10 (2019 to Current)
Chapter 4: Quadratic Equations
Ex.4.20 | Q: 6 | Page no. 76
 NCERT Solution for Mathematics Textbook for Class 10 (2018 to Current)
Chapter 4: Quadratic Equations
Ex.4.20 | Q: 6 | Page no. 76
Solution 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. Concept: Solutions of Quadratic Equations by Factorization.
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