A thermodynamic system is taken from an initial state i with...

A thermodynamic system is taken from an initial state $i$ with internal energy ${U}_{i} = 100J$ 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 ${w}_{af} = 200J, {W}_{ib} = 50J$ and ${W}_{bf} = 100J$ respectively. The heat supplied to the system along the path iaf, ib and bf are iaf ib ${Q}_{iaf}, {Q}_{ib}$ and ${Q}_{bf}$ respectively. If the internal energy of the system in the state b is ${U}_{b} = 200J$ and ${Q}_{iaf} = 500J$ , the ratio $\dfrac{{Q}_{bf}}{{Q}_{ib}}$ is