c
According to an ideal gas equation, the molecular weight of an ideal gas is

\(M=\frac{\rho R T}{P} \quad\left(\text { as } P=\frac{\rho R T}{M}\right)\)

where \(P, T\) and \(\rho\) are the pressure, temperature and density of the gas respectively and \(R\) is the universal gas constant.

\(\therefore\) The molecular weight of \(A\) is

\(M_{A}=\frac{\rho_{A} R T_{A}}{P_{A}}\) and that of \(B\) is \(M_{B}=\frac{\rho_{B} R T_{B}}{P_{B}}\)

Hence, their corresponding ratio is

\(\frac{M_{A}}{M_{B}}=\left(\frac{\rho_{A}}{\rho_{B}}\right)\left(\frac{T_{A}}{T_{B}}\right)\left(\frac{P_{B}}{P_{A}}\right)\)

Here, \(\frac{\rho_{A}}{\rho_{B}}=1.5=\frac{3}{2}, \frac{T_{A}}{T_{B}}=1\) and \(\frac{P_{A}}{P_{B}}=2\)

\(\therefore \quad \frac{M_{A}}{M_{B}}=\left(\frac{3}{2}\right)(1)\left(\frac{1}{2}\right)=\frac{3}{4}\)