Question

The numerator of a fraction is 3less than its denominator.if 2 is aded to both the numerator and the denominator,then the sum of the new fraction and original fraction is29by20.find the original fraction

Answer 1

Let denominator in original fraction be x

so, numerator will be x - 3

so fraction will be (x - 3) / x

Now adding 2 in both we get

denominator = x + 2

numerator = x - 3 + 2 = x - 1

new fraction = (x - 1) / (x + 2)

adding both fractions , we get

(x - 1) / (x + 2) + (x - 3) / x = 29 / 20

or, { x(x - 1 ) + (x + 2)(x - 3) } / (x + 2)x = 29 / 20

or, ( x^2 - x + x^2 -x -6 ) / (x + 2)x = 29 / 20

or,20 ( 2x^2 -2x -6 ) = 29 (x + 2)x

or, 40 (x^2 -x -3) = 29 (x + 2)x

or, 40x²-120-40x=29x²+58x

or, 11x²-98x- 120=0

or, 11x² - 110x +12x -120=0

or, (11x+12)(x-10)=0

value of x we have x=10 ; neglect negative value

Then the required fraction (x-3)/x= 7/10