In the given circuit, the ratio of voltmeter reading to the ammeter reading is R'. If resistance of ammeter is RA, and that of voltmeter RV, then
R=R'+RA
R=R'−RA
RV=R+RA
RV=R−RA
Let current through R be I0 and voltmeter reading is
V0, then R'=V0/I0, also V0=I0 R+RAV0I0=R+RAR'=R+RA ⇒ R=RA −R'