If the speed of rotation of AC generator is made four times of its initial value then what is the percentage increase in induced emf?
In percentage terms it is an increase of 300%.
Induced emf is directly proportional to the rate of change of flux linkage. Since the same AC generator is being used but only running at a faster rate of rotation we know that the magnets and coils are the same . Hence the change in magnetic flux linkage as the coils/magnets rotate is the same . Therefore the only thing changing that affects the rate of change of flux linkage is the rate of rotation.
If the rate of rotation is increased to four times the initial then the rate of flux linkage is increased to four times the initial also. The induced emf is four times greater (it is directly proportional). If it is increased to four times the initial, then in percentage terms that is an increase of 300%. 300% because the initial was 100%, and after the speed increase it is operating at 400%, 400% - 100% = 300%.