A And B can complete a task in 60 days and 40 days respectively. If C, who can complete the same task alone in 30 days, joins A & B working together 3 days after than C joins  them the number of days taken to complete remaining  task will be:

Correct option is A

Given: 

A can complete the work  = 60 days

B can complete  work = 40 days 

C can complete the work = 30 days 

Solution:

Total work = LCM of (60, 40,30) = 120 unit 

Efficiency of A = $$\frac{120}{60} = 2 \ unit/day$$   

Efficiency of B = $$\frac{120}{40 } = 3$$ unit/day

Efficiency of C = $$\frac{120}{30}$$  = 4 unit/day

3 days A and B did = (2+3) x 3 = 15 unit of work
Now C also joins.
All one day work now = 2+3+4 = 9 unit
Remaining work = 120-15 = 105 unit
they will do in =  $$\frac{105}{9}$$​​
                      = $$\frac{35}{3} day$$​s .
=  $$11\frac{ 2}{3}$$​ days taken to complete the task