Question

the numerator of a fraction is 3 less than its denominator. if 2 is added to both the numerator and the denominator, then the sum of the new fraction and original is 29/20.find the original fraction.​

Answer 1

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

  

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