#### 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, form the quadratic equation fo find x.

#### Solution

Given that x denotes the no of toys product in a day

⇒ The cost of production of each by = 55 - no. of toys produced in a day

⇒ (55 - x)

Total cost of production is nothing but product of no. of toys produced in a day and cost of

production of each toy

⇒ x(55 - x)

But total cost of production = Rs 750

⇒ x(55 - x) = 750

⇒ 55x - x^{2} = 750

⇒ 55x - x^{2} - 750 = 0

⇒ -(55x - x^{2} - 750) = 0

⇒ x^{2} -55x + 750 = 0

∴ The required quadratic from of the given data is

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