According to the question,

Since, P can complete a work in 12 days working for 8 hours a day.

Work done in 1 day working for 1 hour a day

P can complete $=\frac{1}{8\times 12}=\frac{1}{96}$^th of the work

Q can complete $=\frac{1}{8\times 10}=\frac{1}{80}$^th of the work

(P+Q) together can complete$=\frac{1}{80}+\frac{1}{96}=\frac{11}{480}$^th of the work

Work done in 1 day working for 8 hours a day

(P+Q) together can complete$=\frac{11\times 8}{480}=\frac{11}{60}$^th of the work

∴  (P+Q) can complete the work in $=\frac{60}{11}=5\frac{5}{11}$ days

Hence option D is the correct.