How is it that Increase in amplitude of electromagnetic radiation results in increase in number of photons

When you increase the amplitude of your light source while keeping the frequency same, you are essentially increasing the power output of the source. However since the energy of individual photons(which depends only on the frequency of the photons) is the same, the number of photons increases correspondingly.

Use:

$mathrm{P}!cdot!mathrm{t} = hnu n$

Where P is the power of the source, n is the no of photons, h is plank's constant and $nu$ is frequency of incident electromagnetic radiation.

Strictly speaking, the amplitude of the field (meaning the operators of the electric and magnetic fields, see here) and the photon number do not commute. Thus, the claims that increasing the amplitude increases the number of photons or vice versa are technically not correct.

The state with definite photon number will have uncertain amplitude, whereas a state with well-dfeined amplitude (a coherent state) will have high uncertainty in the photon number. One however can calculate this uncertainty, which is given by a Poissonian distrubution (see here), and for high amplitudes proportional to the field intensity: $$ (Delta n)^2propto E^2 $$