GATE Electrical Engineering (EE) 2014 Shift 1 Solved Paper

The fuel cost functions of two power plants are
Plant $\mathit{P}1:{\mathit{C}}_1=0.05\mathit{P}{\mathit{g}}_1^2+\mathit{A}\mathit{P}{\mathit{g}}_1+\mathit{B}$
Plant ${\mathit{P}}_2:{\mathit{C}}_2=0.10\mathit{P}{\mathit{g}}_2^2+3\mathit{A}\mathit{P}{\mathit{g}}_2+2\mathit{B}$
Where, P_g1 and P_g2 are the generated powers of two plants, and A and B are the constants. If the two plants optimally share 1000 MW load at incremental fuel cost of 100 Rs/MWh, the ratio of load shared by plants P₁ and P₂ is