A fraction becomes 1/3 when 1 is subtracted from the numerator and it becomes 1/ 4 when 8 is added to its denominator. Find the fraction.

A fraction becomes 1/3 when 1 is subtracted from the numerator and it becomes 1/ 4 when 8 is added to its denominator. Find the fraction.

Let fraction is x/y

A fraction becomes 1/3 when 1 is subtracted from the numerator

So that

Cross multiply we get

3x -3  = y                    …(1)

and it becomes 1/ 4 when 8 is added to its denominator

so that

4x = y + 8

Plug the value of y from equation first we get

4x = 3x – 3 + 8

X = 5

Plug this value back in equation first we get

3*5 – 3  = y

15 – 3 = y

12 = y

Hence fraction is x/y = 5/12