Question

A and B can do a piece of work in 10 days. B and C in 15 days. C and A in 20 days. ALL of them work at it for 2 days, then A leaves. After 2 days of this, B also leaves. C will complete the rest in

Answer 1

A and B together : productivity per day = 1/10.
productivity of  B and C per day = 1/15
productivity of C and A per day = 1/20

add all of them:
   2 * (productivity of A, B and C together) per day = 1/10 + 1/15+ 1/20 = 13/60
           productivity of A, B and C together : 13/120

subtract from this, the productivity of  A and B together. we get
   productivity of C = 13/120 - 1/10 = 1/120
similarly productivity of A = 13/120 - 1/15 = 5/120 = 1/24
productivity of  B = 13/120 - 1/20 = 7/120

All of them work for 2 days: so  13/120  * 2 = 13/60 of work is completed.
Now, B and C work for 2 more days doing 1/15 * 2 = 2/15 work
  work remaining =  1 - 13/60 - 2/15 =  39/60 = 13/20

That will need  C to work for:  (13/120) / (1/120)  = 13 days.