Let present age of P = 5x and present age of Q = 8x According to question, After 3 years, 

$\begin{array}{l}\hspace{0.25em}\hspace{0.25em}\hspace{0.25em}\hspace{0.25em}\frac{5x+3}{8x+3}=\frac{8}{11}\\ \hspace{0.25em}\hspace{0.25em}\hspace{0.25em}\hspace{0.25em}64x+24=55x+33\\ \hspace{0.25em}\hspace{0.25em}\hspace{0.25em}\hspace{0.25em}64x-55x=33-24\\ \hspace{0.25em}\hspace{0.25em}\hspace{0.25em}\hspace{0.25em}9x=9\\ \therefore \hspace{0.25em}\hspace{0.25em}\hspace{0.25em}\hspace{0.25em}x=\frac{9}{9}=1\end{array}$

$\therefore$ Present age of.Q = 8x = 8 x 1 = 8 years.