A alone can do 1/4th of the work in 2 days. B alone can do 2/3rd of the work in 4 days. If all the three work together, they can complete it in 3 days so what part of the work will be completed by C in 2 days ?

A can do the total work in 8 days, and B can do it in 6 days.

Let the total work be 24 units.

Now,
A = 24/8 = 3
B = 24/6 = 4
A + B + C = 24/3 = 8

So Capacity of C = 1 unit.
In two days C will do 2 units which is 2/24^th part of the total work. So 1/12^th part.