If 1 is added to the numerator and to the denominator of a fraction, the value obtained is 4/5. If 5 is subtracted from it's numerator and from it's denominator, the resulting value is 1/2. Find the fraction.

Let n and d represent the numerator and denominator of the fraction.

... (n + 1) / (d + 1) = 4/5

... (n - 5) / (d - 5) = 1/2

Eliminating fractions from these equations gives

... 5 (n + 1) = 4 (d + 1)

... 2 (n - 5) = (d - 5)

Subtracting the first equation from 4 times the second gives

... 4 (2 (n - 5)) - (5 (n + 1)) = 4 (d - 5) - (4 (d + 1))

... 8n - 40 - 5n - 5 = 4d - 20 - 4d - 4

... 3n = 21

... n = 7

... 2 (7 - 5) = d - 5

... 9 = d

The fraction is 7/9.