11a.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 rupees 750. Find the number of toys produced on that day.
Answers
Step-by-step explanation:
Given : Total cost of production of toy = 750
Let the number of toys produced on that day be x.
Therefore the cost of production of each toy that day = (55 - x)
So, the total cost production that day = Number of toys × cost of production of each toy that day
Total cost of production of toy = x × (55 - x)
A.T.Q..
x(55 - x) = 750
55x - x² = 750
-x² + 55x - 750 = 0
x² - 55x + 750 = 0
Hence, the required quadratic equation is x² - 55x + 750 = 0
By factorisation method :
x² - 55x + 750 = 0
x²- 30x - 25x + 750 = 0
x(x - 30) - 25(x - 30) = 0
(x - 30)(x - 25) = 0
x - 30 = 0
x = 30
x - 25 = 0
x = 25
Hence, the number of toys produced (x) = 25 or 30 .
(ii) Let us say, number of toys produced in a day be x.
Therefore, cost of production of each toy = Rs(55 – x)
Given, total cost of production of the toys = Rs 750
∴ x(55 – x) = 750
⇒ x2 – 55x + 750 = 0
⇒ x2 – 25x – 30x + 750 = 0
⇒ x(x – 25) -30(x – 25) = 0
⇒ (x – 25)(x – 30) = 0
Thus, either x -25 = 0 or x – 30 = 0
⇒ x = 25 or x = 30
Hence, the number of toys produced in a day, will be either 25 or 30.