In an ammeter, 5% of the main current passes through the galvanometer. If resistance of the galvanometer is G, the resistance of ammeter will be:

Let total current be I

Given:
current through galvanometer = 5% of I

$$I_g=0.05I$$

So current through shunt:

$$I_s=0.95I$$

step 1: use parallel condition

Voltage across galvanometer = voltage across shunt

$$I_g\cdot G=I_s\cdot R_s$$

$$0.05I\cdot G=0.95I\cdot R_s$$

Cancel I:

$$0.05G=0.95R_s$$

$$R_s=\frac{0.05}{0.95}G=\frac{1}{19}G$$

step 2: equivalent resistance of ammeter

Galvanometer and shunt are in parallel:

$$R_A=\frac{G\cdot R_s}{G+R_s}$$

$$=\frac{G\cdot\frac{G}{19}}{G+\frac{G}{19}}=\frac{G^2/19}{G(1+1/19)}=\frac{G/19}{20/19}=\frac{G}{20}$$