Question

If 2 is added to the numerator of a fraction, it reduces to 1/2 and 1 is subtracted from the denominator , it reduces to 1/3. 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

Answer 2

Answer:

Step-by-step explanation:

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

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