Show that the efficiency of the plant is given by

Question

A working fluid goes through a Carnot cycle of operations, the upper absolute temperature of the fluid being q₁ and the lower absolute temperature being q₂. The amount of heat taken in and rejected by the working fluid are Q₁ and Q₂ respectively. On account of losses of heat due to conduction etc., the heat source temperature T₁ is higher than  and the heat sink temperature T₂ is lower than Q₂. If T₁ = (q₁ + KQ1) ; T₂ = (q₂  – KQ2) where K is the same constant for both the equations, show that the efficiency of the plant is given by 

                                                ${\color{Blue} \eta =1- \frac{T_2}{T_1-K Q_2}}$