Question

A goldsmith desires to test the purity of a gold ornament suspected to the mixed with copper. The ornament weighs $0.25kg$ in air and is observed to displace $0.015l$ of water when immersed in it. Densities of gold and copper with respect to water are, respectively, $19.3$ and $8.9$ The approximate percentage of copper in the ornament is

• A. $5\%$
• B. $10\%$
• C. $13.6\%$
• D. $25\%$

Answer 1

The correct option is C $13.6\%$

We have
$x+y=0.25.......\left(I\right)V_g+V_c=0.015\times {10}^{-3}\because \text{volume of water displaced = volume of (gold+copper)}\Rightarrow \frac{x}{19.3\times {10}^3}+\frac{y}{8.9\times {10}^3}=0.015\times {10}^{-3}\Rightarrow 8.9x+19.3y=19.3\times 8.9\times 0.015\Rightarrow 8.9x+19.3y=2.577.......\left(II\right)\text{solving}\left(I\right)\text{and}\left(II\right),\text{we have}x=0.216kg,y=0.034kg\text{percentage of copper =}\frac{y}{x+y}\times 100=\frac{0.034}{0.216+0.034}\times 100=13.6$