A thermodynamic system is taken from an initial state i with internal energy U_i = 100 J to the final state f along two different paths iaf and ibf, as schematically shown in the figure. The work done by the system along the paths af, ib and bf are W_af = 200 J, W_ib = 50 J and W_bf = 100 J respectively. The heat supplied to the system along the path iaf, ib and bf are Q_iaf, Q_ib and Q_bf respectively. If the internal energy of the system in the state b is U_b = 200 J and Q_iaf = 500 J, the ratio Q_bf / Q_ib is