A fraction becomes $\frac{6}{5}$ when 5 is added to its numerator and becomes $\frac{1}{2}$ when 4 is added to its denominator. The fraction is:

$\frac{7}{10}$

Let us consider that ,

Initially the fraction = \(\frac{x}{y}\)

According to question  ,

\(\frac{x + 5 }{y}\) = \(\frac{6}{5}\)

5x + 25 = 6y   ---(1)

& \(\frac{x  }{y + 4}\) = \(\frac{1}{2}\)

2x = y + 4

2x - 4 = y   ---(2)

Multiply equation 2 by

( 2x - 4 = y ) x 6

 12x - 24  = 6y    ----(3)

subtract equation 1  from equation 3

7x - 49 = 0

x = 7

Now put it into equation 1

5 x 7 + 25 = 6y

60 = 6y

y = 10

So, Original fraction = \(\frac{7}{10}\)