A cottage industry produces a certain number of toys in a day.
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 articles produced in a day. On a particular day, the total cost of production was Rs. 750. If x denotes the number of toys produced that day, from the quadratic equation of find x.

Solution:

Now we know that ‘x’ denotes the total number of toys produced in that day.

But, the cost of production of a single toy is 55 minus the number of toys produced that day i.e. ‘x’.

So, the total production cost would be the product of the cost of a single toy and the total number of toys i.e. product of ‘55 − x’ and ‘x’. Now, it is given here that total production cost of that day was Rs.750.

Therefore,

$(x)(55-x)=750$

$55 x-x^{2}=750$

$x^{2}-55 x+750=0$

Hence, this is the required quadratic equation.