Question

The sum of the numerator and the denominator of the fraction is 12. If 1 is added to both numerator and denominator the fraction becomes 1/2. Find the fraction .

Answer 1

Answer:

let numerator be x

and denominator be

if the sum of x + y=12 _equation 1

then,

added 1 both numerator and denominator

x+1/y+1=1/2 _equation 2

if

x=12-y

put the value of x

12-y+1/y+1=1/2

2(12-y+1)=y+1

24-2y+2-1=y

25=2y+y

25=3y

25/3=y

then put the value of y to find the value of x

x=12-y

x=12-25/3

x=36-25/3

x=11/3

Answer 2

Let the numerator be x and the denominator be (12-x)

A.T.Q:- x+1/12-x+1 = 1/2

           x+1/13-x = 1/2

           2x+2 = 13-x    (cross multiplication)

           2x+2-13+x = 0

           3x-11 = 0

           x = 11/3    (numerator)

           12-x = 12-11/3 = 145/13   (denominator)

            So, the fraction is 11/145.

 Hope you'll find it helpful !!