P can complete the work in (12 x 8) hrs. = 96 hrs.

Q can complete the work in (8 x 10) hrs. = 80 hrs.

So, P's1 hour's work =   \(\frac{1}{96}\)  and Q's 1 hour's work =  \(\frac{1}{80}\) 

(P + Q)'s 1 hour's work =  \(\left(\frac{1}{96}+\frac{1}{80}\right)= \frac{11}{480}\)

So, both P and Q will finish the work in \(\left(\frac{480}{11}\right)\)  hrs.

Therefore, Number of days of 8 hours each = \(\left(\frac{480}{11}\times\frac{1}{8}\right)= \frac{60}{11}days = 5\frac{5}{11}days.\)