Answer:
C) I and III only
Step-by-step explanation:
Let full pool is denoted by O
Days Hose x takes to fill pool O = a
Pool filled in one day x = O/a
Days Hose y takes to fill pool O = b
Pool filled in one day y = O/b
Days Hose z takes to fill pool O = c
Pool filled in one day z = O/c
It is given that
a>b>c

Days if if x+y+z fill the pool together = d
1 day if x+y+z fill the pool together 
I) d < c
d are days when hose x, y, z are used together where as c are days when only z is used so number of days when three hoses are used together must be less than c when only z hose is used. So d < c
III) 
Using (1)

Similarly

So,
