Assume all bulbs are identical, rank the brightness of the bulbs, from brightest to dimmest

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$A > B = C > D = H > E = F = G$

$A > D = H > E = F = G > B = C$

All have equal brightness

$A > D = H > B = C > E = F = G$

answer is A.

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Detailed Solution

For the branch containing A, B and C

$R_{e q} = \frac{3 R}{2}$

Current in A: $I_{1} = \frac{E}{R_{e q}} = \frac{2 E}{3 R}$

Current in each of B and C: $I_{1}^{'} = \frac{I_{1}}{2} = \frac{E}{3 R}$

For the branch containing D, E, F, G and H: $R_{e q} = \frac{7 R}{3}$

Current through D and H: $I_{2} = \frac{E}{R_{e q}} = \frac{3 E}{7 R}$

Current through each of E, F and G: $I_{2}^{'} = \frac{I_{2}}{3} = \frac{E}{7 R}$

Since $I_{1} > I_{2} > I_{1} > I_{2}$

$A > D = H > B = C > E = F = G$

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