The ratio of powers dissipatted respectively in $R$ and $3R$, as shown is:
Diffcult
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Resistors $R$ and $3 R$ are connected in parallel, thus $V_{A B}=V_{C D}$
$\therefore I_{1} R=I_{2}(2 R) \Longrightarrow I_{2}=\frac{I_{1}}{2}$
Current through $3 R, I_{3}=I_{2}+I_{1}=\frac{3}{2} I_{1}$
Ratio of power dissipated in $R$ and $3 R, \frac{P_{1}}{P_{3}}=\frac{I_{1}^{2} R}{I_{3}^{2}(3 R)}=\frac{I_{1}^{2} R}{\left(\frac{3 I_{1}}{2}\right)^{2} \times(3 R)}=\frac{4}{27}$
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