Very good question. The number of quasars must be less than the number of SMBHs, since many galaxies, such as our own, contain SMBHs at their core (Sagittarius A*) and they are not classified as quasars (i.e., some galaxies are quiescent for whatever reason). Quasars represent an ultra-luminous active phase of gas accretion onto the SMBH. Such larger luminosities is believed to be caused by intense gas accretion triggered by major massive scale mergers between galaxies.
As such, Quasars are short lived events, and the SMBHs outlive the quasar (the lifetime of a quasar is of the order of 10$^6$-10$^9$ yr whereas the lifetime of a SMBH is much greater than the Hubble time). Hence, once the gas is all but consumed by such intense accretion the Quasar will slowly become quiescent. Hence why many galaxies contain SMBHs at their cores, but are no longer active.
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