Archimedes' Principle and Buoyant Force Steps:

• The newton meter reading equals the object's weight minus the buoyant force.
• Buoyant force in water: $W - P = \rho_w g V$, where $V$ is displaced volume.
• Buoyant force in oil: $W - Q = \rho_o g V$.
• Ratio of densities: $\frac{\rho_o}{\rho_w} = \frac{W - Q}{W - P}$.

Why D is correct:

• D gives $\frac{W - Q}{W - P}$, the ratio of buoyant forces, equal to the density ratio by Archimedes' principle for equal volumes.

Why the others are wrong:

• A inverts to $\frac{\rho_w}{\rho_w - \rho_o}$, ratio of water density to density difference.

Final answer: D