Mathematics
Solve :
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 750. We would like to find out the number of toys produced on that day.
Quadratic Equations
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Answer
Let no. of toys produced be x.
Cost of each toy = ₹ (55 - x)
Given,
Total cost = 750
⇒ x(55 - x) = 750
⇒ 55x - x2 = 750
⇒ x2 - 55x + 750 = 0
⇒ x2 - 30x - 25x + 750 = 0
⇒ x(x - 30) - 25(x - 30) = 0
⇒ (x - 25)(x - 30) = 0
⇒ x - 25 = 0 or x - 30 = 0
⇒ x = 25 or x = 30.
If x = 25, 55 - x = 30 and,
if x = 30, 55 - x = 35.
Hence, if no. of articles produced are 25 then cost of each article = ₹ 30 and if no. of articles produced are 30 then cost of each article = ₹ 25.
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