A steam chamber is connected to an ice block at $0^{0}C$, by means of two identical rod in series . It is observed that 100 gm of ice is melted in 10 minutes. If they are connected in parallel, the amount of ice melt in 5 minutes in gm is________.

$$\begin{gathered} \mathrm{heat} \mathrm{flow} \mathrm{is} \mathrm{inversely} \mathrm{proportional} \mathrm{to} \mathrm{resistance} \mathrm{and} \mathrm{directly} \mathrm{proportional} \mathrm{to} \mathrm{time} \\ \mathrm{in} \mathrm{the} \mathrm{first} \mathrm{case} \mathrm{resistance} \mathrm{is} 2\mathrm{R} \mathrm{and} \mathrm{time} \mathrm{is} 10 \min \\ \mathrm{in} \mathrm{the} \mathrm{second} \mathrm{case} \mathrm{resistance} \mathrm{is} \raisebox{1ex}{$\mathrm{R}$}\!\left/ \!\raisebox{-1ex}{$2$}\right. \mathrm{and} \mathrm{time} \mathrm{is} 5 \min \\ \mathrm{m}\propto \mathrm{Q}\propto \frac{\mathrm{t}}{\mathrm{R}} \\ \Rightarrow \frac{{\mathrm{m}}_1}{{\mathrm{m}}_2}=\frac{{\mathrm{t}}_1}{{\mathrm{t}}_2}\frac{{\mathrm{R}}_2}{{\mathrm{R}}_1} \\ \Rightarrow \frac{100}{{\mathrm{m}}_2}=\frac{10}{5}\frac{{\displaystyle \raisebox{1ex}{$\mathrm{R}$}\!\left/ \!\raisebox{-1ex}{$2$}\right.}}{2\mathrm{R}}=\frac{1}{2} \\ \Rightarrow m_2=200 \end{gathered}$$