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Quadratic Equations

Question
CBSEENMA10006471
Wired Faculty App

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. We would like to find out the number of toys produced on that day.

Solution

Let the number of toys produced on that day = x
And, cost of production = (55 – x)
According to the given question,
x (55 – x) = 750
⇒ 55x – x2 – 750 = 0
x2 – 55x + 750 = 0
⇒ x2 – 30x – 25x + 750 = 0
⇒ x(x – 30) – 25(x – 30) = 0
⇒ (x – 30) (x – 25) = 0
⇒ x – 30 = 0 or x – 25 = 0
⇒ x = 30 or x = 25.
Hence, the number of toys produced on that day are 30 or 25.

Some More Questions From Quadratic Equations Chapter

Check whether the following are quadratic equations:
x2 – 2x = (–2) (3 – x)

Check whether the following are quadratic equations:
(x – 2) (x + 1) = (x – 1) (x + 3)

Check whether the following are quadratic equations:
(x – 3) (2x + 1) = x(x + 5)

Check whether the following are quadratic equations:
(2x –1) (x–3) = (x + 5)(x–1)

Check whether the following are quadratic equations:
x2 + 3x + 1 = (x – 2)2

Check whether the following are quadratic equations:
(x + 2)3 = 2x(x2 – 1)

Check whether the following are quadratic equations:
x3 – 4x2 – x + 1 = (x – 2)3.

Represent the following problem situations in the form of quadratic equations:
The product of two consecutive positive integers is 306. We need to find the integers.

Represent the following problem situations in the form of quadratic equations:
Rohan’s mother is 26 years older than him. The product of their ages (in years) 3 years from now will be 360. We would like to find Rohan’s present age.

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