Turbojet control volume: air enters at the aircraft's own velocity and ambient density, is heated and accelerated, and leaves as hot exhaust gas at the given exit velocity and area.
Find. The inlet flow area $A_{in}$; the thrust $F$.
Approach. Fuel mass is neglected, so the SAME mass flow rate $\dot{m}$ passes through both the inlet and the exhaust. Compute $\dot{m}$ from the exhaust conditions (density from the ideal gas law at the given $p_0,T_{ex}$, times $A_{ex}V_{jet}$), then use continuity to back out the inlet area from the inlet density and the aircraft's own velocity; finally apply the propulsion thrust relation from the reference sheet.
Aircraft velocity in SI units.
$$V_{ac}=900\ \text{km/hr}=\frac{900\times1000}{3600}=\boxed{250\ \text{m/s}}$$
Mass flow rate from the exhaust station. Treating the exhaust gas as an ideal gas with air's gas constant,
$$\rho_{ex}=\frac{p_0}{RT_{ex}}=\frac{100{,}000}{(287)(973.15)}=0.3580\ \text{kg/m}^3$$
$$\dot{m}=\rho_{ex}A_{ex}V_{jet}=(0.3580)(0.3)(900)=\boxed{96.7\ \text{kg/s}}$$
Inlet area from continuity. Inlet air density at ambient conditions,
$$\rho_{in}=\frac{p_0}{RT_{in}}=\frac{100{,}000}{(287)(293.15)}=1.189\ \text{kg/m}^3$$
Since $\dot m=\rho_{in}A_{in}V_{ac}$,
$$A_{in}=\frac{\dot m}{\rho_{in}V_{ac}}=\frac{96.7}{(1.189)(250)}=\boxed{0.325\ \text{m}^2}$$
Thrust. Using the reference-sheet propulsion relation $F_{thrust}=\dot m(V_{jet}-V_{aircraft})$,
$$F=(96.7)(900-250)=(96.7)(650)=\boxed{62.8\ \text{kN}}$$
