According to the question,

In 1 day,

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

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

 (P+Q) together can complete $=\frac{1}{12}+\frac{1}{8}=\frac{2+3}{24}=\frac{5}{24}$^th of the work

 ∴ (P+Q+R) will complete $\frac{1}{4}$^th of the work

   R can complete (P+Q+R)-(P+Q)

$$\begin{gathered} =\frac{1}{4}-\frac{5}{24} \\ =\frac{6-5}{24}=\frac{1}{24} \end{gathered}$$

 ∴ R will finish the work alone in 24 days.

 Hence option E is the correct.