Question

Question 2(ii)
(ii) A cottage industry produces a certain number of toys in a day. The cost of production of each toy (in rupees) was found to be 55 minus the number of toys produced in a day. On a particular day, the total cost of production was ₹ 750. Find out the number of toys produced on that day.

Answer 1

(ii) Let the number of toys produced be $x$.
$\therefore$ Cost of production of each toy =\( ₹ (55 - x)\)
It is given that, total production of the toys = \(₹ 750\)
$\therefore x(55-x)=750$
$\Rightarrow x^2-55x+750=0$
$\Rightarrow x^2-25x-30x+750=0$
(Splitting the middle term -55x as -25x-30x because $-25x\times -30x=750x^2$)
$\Rightarrow x(x-25)-30(x-25)=0$
$\Rightarrow (x-25)(x-30)=0$
Either, $x-25=0orx-30=0$
$\Rightarrow x=25orx=30$
Hence, the number of toys will be either $25or30$.