JEE Advanced 2014 · Paper 1, Physics question 20

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