Advertisements
Advertisements
प्रश्न
2x articles cost Rs. (5x + 54) and (x + 2) similar articles cost Rs. (10x – 4), find x.
उत्तर
Cost of 2x articles = 5x + 54
Cost of 1 article = `(5x + 54)/(2x)` ….(i)
Again cost of x + 2 articles = 10x – 4
∴ Cost of 1 article = `(10x - 4)/(x + 2)` ...(ii)
From (i) and (ii),
`(5x + 54)/(2x) = (10x - 4)/(x + 2)`
⇒ (5x + 54)(x + 2) = 2x(10x - 4)
⇒ 5x2 + 10x + 54x + 108 - 20x2 - 8x
⇒ 5x2 + 10x + 54x + 108 - 20x2 + 8x = 0
⇒ -15x2 + 72x + 108 = 0
⇒ 5x2 - 24x - 36 = 0 ...(Dividing by -3)
⇒ 5x2 - 30x + 6x - 36 = 0
⇒ 5x(x - 6) + 6(x - 6) = 0
⇒ (x - 6)(5x + 6) = 0
Either x - 6 = 0,
then x = 6
or
5x + 6 = 0,
then 5x = -6
⇒ x = `(-6)/(5)`,
but it is not possible as it is in negative.
∴ x = 6.
APPEARS IN
संबंधित प्रश्न
A two digits number is such that the product of the digits is 12. When 36 is added to the number, the digits inter change their places determine the number.
Solve the following quadratic equations by factorization:
`(2x – 3)^2 = 49`
Solve the following quadratic equation by factorisation.
2m (m − 24) = 50
Find the values of k for which the roots are real and equal in each of the following equation:\[px(x - 3) + 9 = 0\]
If 1 is a root of the quadratic equation \[3 x^2 + ax - 2 = 0\] and the quadratic equation \[a( x^2 + 6x) - b = 0\] has equal roots, find the value of b.
Solve the following quadratic equation using formula method only
x2 - 7x - 5 = 0
The length of the sides forming a right angle in a triangle are 5x cm and (3x-1) cm. If the area of the triangle is 60cm2, find the hypotenuse.
Find two consecutive natural numbers whose squares have the sum 221.
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 equation by factorization
`a/(ax - 1) + b/(bx - 1) = a + b, a + b ≠ 0, ab ≠ 0`
