A can do the work in 10 days.
B can do the work in 15 days.
C can do the work in 20 days.
So, work done by A in one day = 1/10
Work done by B in one day = 1/15
Work done by C in one day = 1/20
So, work done by A and B together in 1 day = 1/10 + 1/15 = 10/60
Work done by B and C together in one day = 1/15 + 1/20 = 7/60
Work done by A and C together in 1 day = 1/10 + 1/20 = 9/60
Now, to get max work in less days, A and B will work on 1st day, A and C on 2nd day ,and B and C on 3rd day.
Total work done in 3 days = 10/60 + 7/60 + 9/60 = 26/60
So, work done in 6 days = 52/60
Remaining work = 8/60
This can be done by A and B together.
They complete 10/60 Work in 1 day.
So, they will take days for 8/60 Work = 60/10 × 8/60 = 4/5 days.
So,total number of days taken = 6 + 4/5 = 6(4/5) days.
Option C