The deflection of galvanometer decreases from 25 divisions to 5 divisions when a resistor of 20Ω is connected in series. What is galvanometer resistance.

5Ω

When resistor $20\Omega$ is not connected, 
From Ohms law $V=IR,$ we get V=25R_G​...(1)    where R_G​= resistance of galvanometer.
When resistor $20\Omega$ is connected,
V = 5(20+R_G​)...(2)
Using Equation 1 and 2,  25R_G​ = 5(20+R_G​)
⇒ 5R_G ​= 20+R_G​
⇒ 4R_G​ = 20 ⇒ R_G​ = 5Ω