Answer
$\dot{m}_{ash}=0.01\ kg/s=315360 kg/year$
$\dot{m}_{gas}=9.99\ kg/s$
Work Step by Step
Assuming 100% efficiency in the separation:
$\dot{m}_{ash}=x_{ash}\dot{m}_t$
$x_{ash}=0.001, \dot{m}_t=10 kg/s$
$\dot{m}_{ash}=0.01\ kg/s$
$\dot{m}_{ash}+\dot{m}_{gas}=\dot{m}_t$
$\dot{m}_{gas}=9.99\ kg/s$
Over an year:
$m_{ash}=\dot{m}_{ash}\Delta t=315360 kg$
