A cottage industry produces a certain number of pottery articles

Leave a Comment / NCERT book maths class 10th, quadratic / By preeti

(Q) 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.

Ans: Let’s the number of articles be $x$

By given condition, cost of production is 3 more than twice the number of articles

hence, cost of production = $2x + 3$

Next, it is given that the total cost of production is Rs. 90

We know that by Cost of production = Number of Articles x Cost of each articles

$\Rightarrow (x) (2 x + 3) = 90$

$\Rightarrow 2 x^2 + 3 x = 90$

$\Rightarrow 2 x^2 + 3 x - 90 = 0$

$\Rightarrow 2 x^2 + 15 x - 12 x - 90 = 0$

$\Rightarrow x (2 x + 15) - 6 (2 x + 15) = 0$

$\Rightarrow (2 x + 15) (x - 6) = 0$

$\Rightarrow x = \frac{- 15}{2} ~ and ~ x = 6$

Here, we reject $x = \frac{-15}{2}$ because the value of the number of the articles can not be a negative number.

Therefore, articles $x = 6$ and cost = $2x + 3 = 2(6) + 3 = 15$

Hence, the number of articles are 6 and cost of each article is Rs. 15.

Check:

If no. of articles are 6 and cost of each article is Rs. 15, let’s check the given condition:

Total cost = 6 x 15 = 90

Since it mees the given condition, hence our answer is correct.

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