Please help me solve this problem. This is for the NGEES PE Mechanical Thermal & Fluids Practice Exam and i have the solution included below also, but i need a more detailed solution with explanations of setting up the problem for better understanding

Known data for a gas turbine$-$steam turbine combined cycle are given with the figure. Neglecting pump work, the thermal efficiency of this combined cycle is most nearly:

A$.42\mathrm{.}2\%$

B$.52\mathrm{.}4\%$

$q=0$

C$.62\mathrm{.}9\%q,$

D$.92\mathrm{.}0\%$

$(1)$

$h_1=124Bt\frac{u}{b}m$

$h_2=272Bt\frac{u}{l}bm$

$h_3=646Bt\frac{u}{l}bm$

$h_4=361Bt\frac{u}{b}m$

$h_5=192Bt\frac{u}{l}bm$

$w_{\text{n}\text{e}\text{t}}=137Bt\frac{u}{b}m$

$W_{\text{n}\text{e}\text{t}}$

$7)1.$HRSG$?(6)$

ST

STEAM TURBINE

$h_6=75Bt\frac{u}{l}bm$

$h_7=1,450Bt\frac{u}{l}bm$

$h_8=970Bt\frac{u}{l}bm$

$m_1^{}(h_4-h_5)=m_6^{}(h_7-h_6)$

$(1)(361-192)=m_6^{}(1,450-75)$

$m_6^{}=0\mathrm{.}123lb\frac{m}{sec}$

${}_{th}=\frac{w_{\text{n}\text{e}\text{t}}^{}}{q_{in}}=\frac{(1)(137)+(0\mathrm{.}123)(1,450-970)}{(1)(646-272)}$

$,=\frac{137+59}{374}=52\mathrm{.}4\%$

THE CORRECT ANSWER IS: B