Question

The numerator of a fraction is 3 less than its denominator if 2 is added to the both numerator and denominator then the sum of new fraction and original fraction is 29/30 find the original fraction

Answer 1

Answer ; Let the denominator be x

Numerator is x-3

The fraction is (x-3)/x

when 2 is added to numerator and denominator

we have fraction as (x-1)/(x+2)

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

⇒ (x-3)((x+2) +x(x-1)=x(x+2)*29/20

⇒ (x²-6-x + x²-x)20= 29x²+58x

⇒ 40x²-120-40x=29x²+58x

⇒ 11x²-98x- 120=0

⇒ 11x² - 110x +12x -120=0

⇒ (11x+12)(x-10)=0

Canceling the negative fraction value of x we have x=10

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