How can I increase the rpm of an electric motor

Is there something specific your trying to do or is this a homework question ?

Yeah, actually I work in a factory and we are trying to increase the motor speed which drives an agitator used to mix paints

There are 2 ways to do it.

1) increase voltage.

2) adjust the armature.

Just becareful because if you adjust the armature too much you can lose the torque of the motor and cause it to overheat under load.

One other solution would be to change to a pulley system and the by changing diameter of the pulley would change the speed.

Have you considered changing your pulley?