A thermodynamic system is taken form an initial state i with internal energy $\mathrm{U}_{\mathrm{i}}=100 \mathrm{~J}$ to the final state f along two different paths iaf and ibf, as schematically shown in the fire. The work done by the system along the paths $\mathrm{af}, \mathrm{ib}$ and bf are $\mathrm{W}_{\mathrm{af}}=200 \mathrm{~J}, \mathrm{~W}_{\mathrm{ib}}=50 \mathrm{~J}$ and $\mathrm{W}_{\mathrm{bf}}=100 \mathrm{~J}$ respectively. The heat supplied to the system along the path iaf, ib and bf are $Q_{\text {iff }}, Q_{\text {bf }}$ and $Q_{\text {b }}$ respectively. If the internal energy of the sytem in the state $b$ is $U_b=$ 200 J and $Q_{i f f}=500 \mathrm{~J}$, the ratio $Q_{b t} / Q_{i b}$ is: