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Question -

A cottage industryproduces a certain number of pottery articles in a day. It was observed on aparticular day that the cost of production of each article (in rupees) was 3more than twice the number of articles produced on that day. If the total costof production on that day was Rs.90, find the number of articles produced andthe cost of each article.



Answer -

Let us say, the number of articles producedbe x.

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

Given, total cost of production is Rs.90

∴ x(2x + 3) = 90

⇒ 2x2 + 3x – 90 = 0

⇒ 2x2 + 15x -12x –90 = 0

⇒ x(2x + 15) -6(2x + 15) = 0

⇒ (2x + 15)(x – 6) = 0

Thus, either 2x + 15 = 0 or x –6 = 0

⇒ x = -15/2 or x = 6

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

Hence, number of articles produced = 6

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

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