Question

A fraction becomes 4/5 if 1 is added to both numerator and denominator . If however, 5 is subtracted from both numerator and denominator, the fraction becomes 1/2. Find the fraction.

Answer 1

let the fraction be x/y
1 is added means
x+1/y+1=4/5
5x+5=4y+4
5x-4y=-1
5 is subtracted means
x-5/y-5=1/2
2x-y=5
2 eqn multilply by 5 and 1 eqn by 2
2(5x-4y=-1)=10x-8y=-2
5(2x-y=5)=10x-5y=25
10x-5y=25
10x-8y=-2
x=7,y=9
then the fraction  is 7/9

Answer 2

Let the fraction be p/q
give that the fraction will become 4/5 if 1 is added to numerator and denominator
so
4/5 =(p+1)/(q+1)
4q+4 = 5p+5
and
(p-5)/(q-5)=1/2
2p-10=q-5
q= 2p-5
SO
    4(2p-5) +4 =5p+5
   8p-20+4 = 5p+5
    3p= 21
    p=7
Therefore q=2*7-5
          q=9
So the fraction is 7/9