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 to find x.

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25 or 30

26 or 30

25 or 35

26 or 35

answer is A.

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Detailed Solution

Given,
Total production of the toys = Rs 750
Assume that the number of toys produced be x.
Therefore, Cost of production of each toy = Rs. (55-x).
According to the question,

⇒ x (55 − x) = 750 ⇒ x 2 − 55 x + 750 = 0 ⇒ x 2 − 25 x − 30 x + 750 = 0 ⇒ x (x − 25) − 30 (x − 30) = 0

⇒ (x − 25) (x − 30) = 0 ⇒ x − 25 = 0 or x − 30 = 0

Therefore,

x = 25

x = 30

.
Hence the number of toys produced that day will be either 25 or 30.
So, the correct option is 1.

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