Find a fraction which becomes when 1 is subtracted from the numerator and 2 is added to the denominator, and the fraction becomes when 7 is subtracted from the numerator and 2 is subtracted from the denominator.

Let the fraction be x/y.

According to question -

On Cross multiplying, we get -

⇒ 2x - 2 = y + 2

⇒ 2x - y = 4.....(1)

and,

On Cross multiplying, we get -

3x - 21 = y - 2

⇒ 3x - y = 19.....(2)

Subtracting equation (1) from equation (2), we get -

⇒ x = 15

Substituting the value of x in equation (1), we get -

y = 26

Thus, the required fraction is 15/26.