Lets say the fraction is "x/y" ("x" is numerator and "y" is denominator).

If "3" is subtracted from the numerator of a certain fraction, the value of the fraction becomes "3/5" means:

(x - 3)/y = 3/5 cross-multiply

5(x - 3) = 3y

If "1" is subtracted from the denominator of the same fraction, the value of the fraction becomes "2/3" means:

x/(y - 1) = 2/3 cross-multiply

3x = 2(y - 1)

We need to solve the following system of equations:

5(x - 3) = 3y

3x = 2(y - 1)

........

Click here to see the step by step solution

........

x = 36

y = 35

The original fraction is 36/35.