According to the question,

In 1 day

Manoj can complete $\frac{1}{12}$^th of the work 

Salim can complete $\frac{1}{8}$^th of the work

∴ Raj can complete$=2\times \frac{1}{8}=\frac{1}{4}$ ^th of the work

Then, (Manoj+Salim+Raj) can complete 

$$\begin{gathered} =\frac{1}{12}+\frac{1}{8}+\frac{1}{4} \\ =\frac{2+3+6}{24}=\frac{11}{24} \end{gathered}$$

∴  (Manoj+Salim+Raj)'s together will complete the work in $\frac{24}{11}$ or $2\frac{2}{11}$ days.

 Hence option E is the correct.