Let us assume that our galaxy consists of 2.5 x 10¹¹ stars each of one solar mass. How long will a star at a distance of 50,000 ly from the galactic centre take to complete one revolution? Take the diameter of the Milky way to be 10⁵ ly.

Mass of our galaxy Milky Way, M = 2.5 × 10¹¹ solar mass
Solar mass = Mass of Sun = 2.0 × 10³⁶ kg
Mass of our galaxy, M = 2.5 × 10¹¹ × 2 × 10³⁶ = 5 × 10⁴¹ kg
Diameter of Milky Way, d = 10⁵ ly
Radius of Milky Way, r = 5 × 10⁴ ly
1 ly = 9.46 × 10¹⁵ m
∴r = 5 × 10⁴ × 9.46 × 10¹⁵
= 4.73 ×10²⁰ m
Since a star revolves around the galactic centre of the Milky Way, its time period is given by the relation:
T = ( 4π²r³ / GM)^1/2
= [ (4 × 3.14² × 4.73³ × 10⁶⁰) / (6.67 × 10^-11 × 5 × 10⁴¹) ]^1/2
=   (39.48 × 105.82 × 10³⁰ / 33.35 )^1/2
= 1.12 × 10¹⁶ s
1 year = 365 × 324 × 60 × 60 s
1s = 1 / (365 × 324 × 60 × 60)  years
∴ 1.12 × 10¹⁶ s = 1.12 × 10¹⁶ / (365 × 24 × 60 × 60)  =  3.55 × 10⁸ year