b
$\frac{\text { Power in }(\mathrm{P}+\mathrm{Q})}{\text { Power in }(\mathrm{R}+\mathrm{S})}=\frac{\frac{\mathrm{V}^{2}}{\mathrm{P}+\mathrm{Q}}}{\frac{\mathrm{V}^{2}}{\mathrm{R}+\mathrm{S}}}=\frac{\mathrm{R}+\mathrm{S}}{\mathrm{P}+\mathrm{Q}}$
$=\frac{\mathrm{R}\left[1+\frac{\mathrm{S}}{\mathrm{R}}\right]}{\mathrm{P}\left[1+\frac{\mathrm{Q}}{\mathrm{P}}\right]}$ ........$(A)$
Also $\frac{\mathrm{P}}{\mathrm{R}}=\frac{\mathrm{Q}}{\mathrm{S}} \Rightarrow \frac{\mathrm{S}}{\mathrm{R}}=\frac{\mathrm{Q}}{\mathrm{P}}$ ...........$(B)$
from $(A)$ and $(B)$
$\frac{\text { Power in }(\mathrm{P}+\mathrm{Q})}{\text { Power in }(\mathrm{R}+\mathrm{J})}=\frac{\mathrm{R}}{\mathrm{P}}$