a/b < c/d
as a, b, c and d are positive integers, rearranging the terms of the inequality
a/c < b/d
Adding 1 to each side of the inequality
a/c + 1 < b/d + 1
(a+c)/c < (b+d)/d
(a+c)/(b+d) < c/d

I. (a+c)/(b+d) < c/d This is always true

II. (a+c)/(b+d) < a/b
(a+c)/(b+d) is less than c/d but whether it is less than a/b is not known. Not always true

III. (a+c)/(b+d) = a/b + c/d
As (a+c)/(b+d) < c/d, left hand side cannot be equal to the right hand side. False

IMO B