Let fast per day be x, no of days required to show correct time

for condition 1 is     2 / x. 

For condition 2 is     3 / (x + 1/2)

Condition 2 is one day sooner hence 2 / x  =  3 / (x + 1/2)   +  1

Solving this we will get x^2 +1.5 x - 1 = 0

x = -2 or +1/2.  It is running fast hence x = 1/2

Hence the answer is 1/2 min per day.

To verify this for condition 1 it require 4 days ( 2 % 1/2 )

Condition 2 it require 3 days [ 3 % (1/2 + 1/2 )]  i.e 1 day less than condition 1.