Question

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 Rs 750. Find out the number of toys produced on that day.
[2 Marks]

Answer 1

Let the number of toys produced be $x$.
$\therefore$ Cost of production of each toy =$Rs(55-x)$
[0.5 Marks]

It is given that, total production of the toys = $Rs750$
$\therefore x(55-x)=750$ [0.5 Marks]
$\Rightarrow x^2-55x+750=0$
$\Rightarrow x^2-25x-30x+750=0$
$\Rightarrow x(x-25)-30(x-25)=0$
$\Rightarrow (x-25)(x-30)=0$ [0.5 Marks]
Either, $x-25=0orx-30=0$
$\Rightarrow x=25orx=30$
Hence, the number of toys will be either $25or30$.
[0.5 Marks]