$3)$ Two reversible heat engines, $\backslash ($ A $\backslash )$ and $\backslash ($ B $\backslash ),$ are connected in series between two thermal reservoirs at $\backslash (727^\{\backslash$circ$\}\backslash$mathrm$\{$C$\}\backslash )$ and $\backslash (-173^\{\backslash$circ$\}\backslash$mathrm$\{$C$\}\backslash ).$ Engine A receives $1675$ kJ of heat from high temperature reservoir and rejects heat to engine B$.$ Engine B takes the heat from $\backslash ($ A $\backslash )$ and rejects to low temperature reservoir $($look at the figure below$).$

a$)$ If engines have the same efficiency, determine the work outputs of engines A and $\backslash ($ B $\backslash ).$

b$)$ If engines deliver equal amount of work, determine the efficiencies of the engines.