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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. We would like to find out the number of toys produced on that day.
Solution
Let the number of toys produced be x.
∴ Cost of production of each toy = Rs (55 − x)
It is given that the total 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
Either x − 25 = 0 or x − 30 = 0
⇒ x = 25 or x = 30
Hence, the number of toys will be either 25 or 30.
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