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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.
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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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