Two reversible heat engines \(A\) and \(B\) are arranged in series. A rejects heat directly to \(B\). Engine \(A\) receives \(300 \mathrm{~kJ}\) at a temperature of \(500^{\circ} \mathrm{C}\) from the heat source, while engine \(B\) is in communication with a cold sink at a temperature of \(5^{\circ} \mathrm{C}\). If the work output of \(A\) is twice that of \(B\), calculate

(a) the intermediate temperature between \(A\) and \(B\), and

(b) thermal efficiency of each engine.