In a galvanometer 5% of the total current in the circuit passes through it. If the resistance of the galvanometer is G, the shunt resistance ‘S’ connected to the galvanometer is

Let I be the total current passing through it.

The current passing through the galvanometer is $I_G=0.05I$

And the current passing through the shunt resistance is $I_s=I-0.05I$

$I_s=0.95I$

Since 5% of the total current passes through the galvanometer, the current through the shunt resistance is:

$I_{s}S=I_{G}G$

$\frac{S}{G}=\frac{0.05}{0.95}=\frac{1}{10}$

$S=\frac{G}{19}$

Hence the correct answer is $\frac{G}{19}.$