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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

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