A is 50% as efficient as B. C does half of the work done by A and B together in the same time. If C alone does the work in 20 days, then A, B and C together can do the same work in:

\(6\frac{2 }{3}\)days

ATQ, C's efficiency is half of the efficiency of (A +  B)

Therefore, 

                  A  :   B    :  C    

Efficiency :  1   :   2   :  3 × \(\frac{1}{2}\)

                  2   :   4   :  3

Now,

                  C   :   A + B + C 

Efficiency :   3   :        9

Time       :   9    :       3

                  3    :       1     

C does the work in 20 days 

⇒ 3R = 20

Time takn by (A + B + C) = 1R = \(\frac{20}{3}\) = 6\(\frac{2}{3}\)