Step-by-step explanation:

Let the fraction be

y

x

.

The fraction becomes

2

1

when denominator is increased by 4.

Therefore,

y+4

x

=

2

1

⇒2x=y+4

2x−y=4 ....(1)

Now, the fraction is equal to

8

1

when numerator is diminished by 5.

Therefore,

y

x−5

=

8

1

⇒8x−40=y

⇒8x−y=40 ....(2)

Subtracting equations (1) and (2), we get

6x=36

⇒x=6

Putting this value in equation (1), we get

2(6)−y=4

⇒12−y=4

⇒y=8

Therefore, the fraction is

8

6