Three persons Ram, Ali and Peter were to be hired to paint a house. Ram and Ali can paint the whole house in $$30$$ days, Ali and Peter in $$40$$ days while Peter and Ram can do it in $$60$$ days. If all of them were hired together, in how many days can they all three complete $$ 50\% $$ the work?

Let the working rates of Ram, Ali and Peter be $$R,A$$ and $$P$$ respectively

$$R+A=\dfrac{1}{30}$$

$$A+P=\dfrac{1}{40}$$

$$R+P=\dfrac{1}{60}$$

Adding the three pairwise rates gives:

$$2(R+A+P) = \frac{1}{30}+\frac{1}{40}+\frac{1}{60} = \frac{3}{40}$$

So the combined rate is $$R+A+P = \frac{3}{80}$$ of the work per day. 

The time for all three working together to finish the whole house is $$=\frac{80}{3} = 26\frac{2}{3}$$ days.