Question

A cottage industry produces a certain number of articles in a day. It was observed on a particular day that the cost of production of each article (in ₹) was 7 more than twice the number of articles produced on that day. Find the number of articles produced, if the total cost of production on that day was ₹ 114.

• A. 6
• B. 8
• C. 10
• D. 5

Answer 1

The correct option is A 6

Let the number of articles produced $=x$

Given that the cost of production of each article (in ₹) was 7 more than twice the number of articles produced on that day.

So that the cost of production of each article $=₹(2x+7)$

Given that If the total cost of production on that day was ₹ 114.

So that production cost = ₹ 114

$\Rightarrow x(2x+7)=114$

$\Rightarrow 2x^2+7x–114=0$


For a quadratic equation $a{x}^2+bx+c$,
$x=\frac{-b\pm \sqrt{b^2-4ac}}{2a}$

Here $a=2,b=7$ and $c=-114$

So, $x=\frac{-7\pm \sqrt{(7{)}^2-4\times 2\times -114}}{2\times 2}$

$x=\frac{-7\pm \sqrt{961}}{2}=\frac{-7\pm 31}{4}$

$x=6orx=-9.5$

$x$ cannot be a negative value. So $x=6$

Hence, no. of articles produced = 6