Question

A fraction becomes 1/3 if 1 is subtracted from both its numerator and denominator . If 1 is added to both numerator and denominator, it becomes 1/2. Find the fraction.

Answer 1

x-1/y-1=1/3.....1
x+1/y+1=1/2....2
  from 1
   3x-y=2...3
from 2
  2x-y=-1....4
subtracting     3 from 4
        2x-y+y-3x=-1-3
       x=1 
  putting the value of x in 3
   
     3-y=2
 y=1
  so the fraction is 1/1

Answer 2

Let the fraction be p/q
(p-1)/(q-1) = 1/3
(p+1)/(q+1) = 1/2
3p - 3 = q -1 ⇒ 3p -2 = q 
2p +2 = q +1 ⇒ 2p + 1 = q
3p -2 = 2p +1
p = 3 ⇒ p = 3
q= 6+1 = 7
So the fraction p/q is 3/7