Question

A fraction becomes `1/3` when 2 is subtracted from the numerator and it becomes `1/2` when 1 is subtracted from the denominator. Find the fraction.

Answer 1

Let's assume  the fraction be `"x"/"y"`
First condition:
`(X-2)/y =1/3`
⇒ 3x -6 = y
⇒ 3X - Y= 6      ............. (1)
second condition:
`x/(y-1)= 1/2`
⇒ 2x = y- 1
⇒ 2x - y = -l ............ (2)
Using eliminated method:

Multiplying : (2) by -1 and then adding (1) and (2)
⇒  3x- y = 6
⇒  - 2x + y = 1

⇒  x = 7 
Now, from (1),
⇒  3x - y =6

⇒  3(7) - y = 6
⇒  21 - y  =6
⇒  y = 15

∴ x = 7, y = 15