Answer
$\dfrac{\dot{m}_s}{\dot{m}_s}=0.246$
Work Step by Step
From table A-6:
Steam inlet ($P_1=1\ MPa, T_1=200°C$): $h_1=2828.3\ kJ/kg$
Steam outlet ($P_2=1\ MPa, x_2=0$): $T_2=179.9°C,\ h_2=762.51\ kJ/kg$
Feedwater inlet ($P_3=2.5\ MPa, T_3=50°C$): $h_3=209.34\ kJ/kg$
Feedwater outlet ($P_4=2.5\ MPa, T_4=T_2-10$): $h_4=718.55\ kJ/kg$
From the energy balance:
$\dot{m}_sh_1+\dot{m}_fh_3=\dot{m}_sh_2+\dot{m}_fh_4$
$\dot{m}_s(h_1-h_2)=\dot{m}_f(h_4-h_3)$
$\dfrac{\dot{m}_s}{\dot{m}_s}=\dfrac{h_4-h_3}{h_1-h_2}$
$\dfrac{\dot{m}_s}{\dot{m}_s}=0.246$
