Question

the numerator of a fraction is 4 less than the denominater. if 1 is added to both it's numerator and denominator, it becomes 1/2.find the fraction.

Answer 1

let denominator of the fraction be x.
then numerator =(x-4)
ATQ
if 1 is added to both the the fraction becomes 1/2

so,?(x-4+1)/(x+1)=1/2
2(x-3)=x+1 [by cross multiplication]
2x-6=x+1
2x-x=1+6
x=7

so,numerator =7-4=3
denominator=7

fraction is 3/7

Answer 2

Let the denominator be x.
so, numerator = x-4 

a/q         x-4+1 / x+1 = 1/2
           ⇒ 2( x-3) = x+1
           ⇒ 2x -6  = x +1
           ⇒  2x - x = 1+6
           ∴  x = 7

so, the denominator = 7
numerator =  7-4 = 3

and therefore, the fraction is 3/7

we can also write numerator = x and denominator = x+4 . then also, answer will be same.