A piece brass (Cu and Zn) weight 12.9 g in air. When completely immersed in water, it weight 11.3 g. The relative densities of Cu and Zn are 8.9 and 7.1 respectively. Calculate the mass of copper in the alloy

If the alloy has m g of copper, then $(12.9-\mathrm{m})$ g of zinc will be present. Therefore, the volumes of copper and zinc will be,

${\mathrm{V}}_{\mathrm{Cu}}=\frac{\mathrm{m}}{{\mathrm{\rho }}_{\mathrm{Cu}}} \& {\mathrm{V}}_{\mathrm{Zn}}=\frac{12.9-\mathrm{m}}{{\mathrm{\rho }}_{\mathrm{Zn}}}$

Thus the total volume of alloy,

$\mathrm{V}={\mathrm{V}}_{\mathrm{Cu}}+{\mathrm{V}}_{\mathrm{Zn}}=\frac{\mathrm{m}}{8.9}+\frac{(12.9-\mathrm{m})}{7.1}\mathrm{\_\_\_\_\_}\left(1\right)$

12.9 - m g of zinc will be present in the alloy if it has m g of copper. 

The volumes of copper and zinc will be the amount of water displaced

$= (12.9 - 11.3) \mathrm{g} \mathrm{or} \mathrm{V} = 1.6 \mathrm{cc\_\_\_\_\_\_\_\_}\left(2\right)$

When we solve for m by substituting V from equation (ii) in I we obtain m = 7.61 g.

Hence the correct answer is 7.6gm.