Question

A cottage industry produces a certain number of pottery articles in a day. It was observed on a particular day that cost of production of each articles (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 articles.​

Answer 1

$\huge\underline\mathbb {SOLUTION:-}$

Answer:

• The number of articles produced is 6.
• The cost of each articles is Rs.15

Given:

• The total cost of production is Rs.90

Need To Find:

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

Explanation:

$\mathsf {Let\:cost\:of\:articles\:be\:Rs\:x.}$

$\underline \textbf {Therefore :}$

Cost of production of each article = Rs (2x + 3)

• The total cost of production = Number of pottery articles produced × Cost of production

$\underline\mathsf \red {According\:to\:the\:question \: :-}$

$\textbf { 90 = x (2x + 3) = 0}$

$\implies \mathsf {2x^2+ 3x - 90 = 0}$

$\implies \mathsf {2x^2 + 15x -12x - 90 = 0}$

$\implies \mathsf {x(2x + 15) - 6(2x + 15) = 0}$

$\implies \mathsf {(2x + 15)(x - 6) = 0}$

$\underline\mathsf \blue {Now\: :-}$

$\implies \mathsf {2x + 15 = 0}$

$\implies \mathsf {2x = - 15}$

$\implies \mathsf {x = \frac{-15}{2}}$

$\implies \mathsf {x - 6 = 0}$

$\implies \mathsf {x = 6}$

$\implies \mathsf { x = \frac{-15}{2}\: Or\:x = 6}$

As the number of articles produced can only be a positive integer,

Therefore, x can only be 6.

$\underline\mathsf \pink {Hence\: :-}$

• Number of articles produced = 6
• Cost of each article = 2 × 6 + 3 = Rs 15.

Answer 2

Answer:

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