A and B together can do a piece of work in 36 days, B and C together can do it in 24 days. A and C together can do it in 18 days. The three working together can finish the work in

Let total work to be done = 72 units

Let the efficiency of A, B and C alone be $$a,b$$ and $$c$$ units/day respectively.

A and B together can do work in 36 days

=> $$a+b=\frac{72}{36}=2$$ units/day

Similarly, $$b+c=\frac{72}{24}=3$$ units/day

and $$a+c=\frac{72}{18}=4$$ units/day 

Adding the above three equations, we get :

=> $$2(a+b+c)=2+3+4=9$$

=> $$a+b+c=\frac{9}{2}=4.5$$

$$\therefore$$ Time taken by all of them to finish the work together = $$\frac{72}{4.5}=16$$ days

=> Ans - (B)