Let the total number of shots be $ x $. Then,

Shots fired by A =$ \dfrac{5}{8} x $

Shots fired by B =$ \dfrac{3}{8} x $

Killing shots by A =$ \dfrac{1}{3} $of$ \dfrac{5}{8} x $=$ \dfrac{5}{24} x $

Shots missed by B =$ \dfrac{1}{2} $of$ \dfrac{3}{8} x $=$ \dfrac{3}{16} x $

$\therefore \dfrac{3x}{16} $= 27 or $ x $ =$ \left(\dfrac{27 \times 16}{3} \right) $= 144.

Birds killed by A =$ \dfrac{5x}{24} $=$ \left(\dfrac{5}{24} \times 144\right) $= 30.