Advertisements
Advertisements
प्रश्न
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.
उत्तर
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.
संबंधित प्रश्न
In a class test, the sum of Shefali’s marks in Mathematics and English is 30. Had she got 2 marks more in Mathematics and 3 marks less in English, the product of their marks would have been 210. Find her marks in the two subjects
Solve the following quadratic equations by factorization:
`(x-1)/(x-2)+(x-3)/(x-4)=3 1/3`, x ≠ 2, 4
Find the two consecutive natural numbers whose product is 20.
Solve the following quadratic equations by factorization:
`(2x – 3)^2 = 49`
Two natural number differ by 3 and their product is 504. Find the numbers.
Solve the following quadratic equation for x:
x2 − 4ax − b2 + 4a2 = 0
A quadratic equation whose one root is 2 and the sum of whose roots is zero, is ______.
The hypotenuse of a grassy land in the shape of a right triangle is 1 m more than twice the shortest side. If the third side is 7m more than the shortest side, find the sides of the grassy land.
Solve equation using factorisation method:
x(x – 5) = 24
Five years ago, a woman’s age was the square of her son’s age. Ten years later her age will be twice that of her son’s age. Find:
The present age of the woman.
Solve the following quadratic equation by factorisation:
2x2 + ax - a2 = 0 where a ∈ R.
Solve the following by reducing them to quadratic form:
`sqrt(y + 1) + sqrt(2y - 5) = 3, y ∈ "R".`
In each of the following determine whether the given values are solutions of the equation or not.
x2 + `sqrt(2)` - 4 = 0; x = `sqrt(2)`, x = -2`sqrt(2)`
Solve the following equation by factorization
`(x^2 - 5x)/(2)` = 0
Solve the following equation by factorization
`(1)/(2a + b + 2x) = (1)/(2a) + (1)/b + (1)/(2x)`
In a certain positive fraction, the denominator is greater than the numerator by 3. If 1 is subtracted from both the numerator and denominator, the fraction is decreased by `(1)/(14)`. Find the fraction.
The hotel bill for a number of people for an overnight stay is Rs. 4800. If there were 4 more, the bill each person had to pay would have reduced by Rs. 200. Find the number of people staying overnight.
A farmer wishes to grow a 100 m2 rectangular vegetable garden. Since he has with him only 30 m barbed wire, he fences three sides of the rectangular garden letting compound wall of his house act as the fourth side fence. Find the dimensions of his garden.
Complete the following activity to solve the given quadratic equation by factorization method.
Activity: x2 + 8x – 20 = 0
x2 + ( __ ) – 2x – 20 = 0
x (x + 10) – ( __ ) (x + 10) = 0
(x + 10) ( ____ ) = 0
x = ___ or x = 2
Is 0.2 a root of the equation x2 – 0.4 = 0? Justify
