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The numerator of a fraction is 3 less than denominator. If 2 is added to both numerator as well as denominator, then sum of the new and original fraction

is 29/20. Find the fraction.


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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