To determine the composition of a bimetallic alloy, a sample is first weighed in air and then in water. These weights are found to be $w_1$ and $w_2$ respectively. If the densities of the two constituent metals are $\rho_1$ and $\rho_2$ respectively, then the weight of the first metal in the sample is (where $\rho_w$ is the density of water):

• A
  $\frac{\rho_1}{\rho_w(\rho_2-\rho_1)}[w_1(\rho_2-\rho_w)-w_2 \rho_2]$
• B
  $\frac{\rho_1}{\rho_w(\rho_2+\rho_1)}[w_1(\rho_2-\rho_w)+w_2 \rho_2]$
• C
  $\frac{\rho_1}{\rho_w(\rho_2-\rho_1)}[w_1(\rho_2+\rho_w)-w_2 \rho_1]$
• D
  $\frac{\rho_1}{\rho_w(\rho_2-\rho_1)}[w_1(\rho_1-\rho_w)-w_2 \rho_1]$