Question

if 2 is added to the numerator of a fraction it becomes 1 by 2 and if 1 is subtracted from the denominator it becomes 1 by 3 find the fraction​

Answer 1

Let the fraction be x/y. Then by the given question,
(x+2)/y=x/y-1/2
or, (x+2)/y-x/y=-1/2
or,( x+2-x)/y=-1/2
or, 2/y=-1/2
or, y/2=-2
or, y=-4
x/(y-1)=x/y-1/3
or, x/(-4-1)=x/(-4)-1/3
or, -x/5=-x/4-1/3
or, -x/5+x/4=-1/3
or, (-4x+5x)/20=-1/3
or, x/20=-1/3
or, x=-20/3
then, x/y=(-20/3)/-4=5/3