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# Ex.4.2 Q6 Quadratic Equations Solutions - NCERT Maths Class 10

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## Question

A cottage industry produces 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 cost of the production on that day is ₹ $$90,$$ find the number of articles produced and the cost of each article.

Video Solution
Ex 4.2 | Question 6

## Text Solution

What is known?

(i) On a particular day that cost of production of each article (in rupees) was $$3$$ more than twice the no. of articles produced on that day.

(ii) The total cost of the production is ₹ $$90.$$

What is Unknown?

Number of articles produced and cost of each article.

Reasoning:

Let the number of articles produced on that day be $$x.$$

Therefore, the cost (in rupees) of each article will be $$(3 + 2x)$$

Total cost of production $$=$$ Cost of each article $$\times$$ Total number of articles

$90{\rm{ }} = {\rm{ }}\left( {3{\rm{ }} + {\rm{ }}2x} \right)\left( x \right)$

Steps:

\begin{align}90 &= \left( {3 + 2x} \right)\left( x \right)\\\left( {3 + 2x} \right)\left( x \right) &= 90\\ 3x + 2x^2 &= 90 \end{align}

\begin{align} 2x^2 + 3x-90 &= 0\\ 2x^2 \!\! + \!\! 15x \!- \! 12x \!-90 &= 0\\ \left(\! {2x + 15} \! \right) \! - \! 6 \! \left( 2x \! +\! 15 \right) & = 0\\\left( {2x + 15} \right)\left( {x - 6} \right) &= 0\end{align}

\begin{align} 2x + 15 = 0 &\qquad x-6 = 0\\2x = - 15 &\qquad x = 6\\x = - \left(\frac{15}{2}\right)&\qquad x = 6\end{align}

Number of articles cannot be a negative number.

$\therefore \,\,x = 6$

Cost of each article

\begin{align}& = {\rm{ }}3{\rm{ }} + {\rm{ }}2x\\& = {\rm{ }}3{\rm{ }} + {\rm{ }}2{\rm{ }}\left( 6 \right)\\& = {\rm{ Rs}}{\rm{. }}\,15 \end{align}

Cost of each article is $$\rm{Rs.}\,15.$$

Number of articles produced is $$6.$$

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