BJT Circuit Analysis Problem
The solution is correct. Once \$ V_{ce} \approx 0.2V\$, the transistor is pushed to the saturation region and a maximum current, \$ I_{csat} \$ will flow in the collector circuit. When it is in the saturation region, increase in \$ I_{B} \$ will have no effect on \$I_C \$ anymore. It will only push the transistor deeper into saturation. So \$ I_B \$ can be greater than \$ I_C\$ in such circuits.