A goldsmith desires to test the purity of a gold ornament suspected to the mixed with copper. The ornament weighs 0.25 kg in air and is observed to displace 0.015 litre 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

Weight of ornament in air = 0.25 kg
weight of displaced water = $=0.015\times {10}^{-3}\times \mathrm{\rho kg}$, where $\rho$ is the density of water.
Hence, the relative density of the ornament is $0.25/\left(0.015\times {10}^{-3}\times \mathrm{\rho }\right)$.
Let the percentage of copper in the ornament be n%. Then the relative density of ornament is

$\frac{1}{100}\left[\right(100-\mathrm{n})19.3+8.9\mathrm{n}]=\frac{1}{100}[1930-10.4\mathrm{n}]$

Hence,

$\begin{array}{l} \frac{1}{100}[1930-10.4\mathrm{n}]=\frac{0.25}{0.015\times {10}^{-3}\times {10}^3}=\frac{50}{3}\\ \Rightarrow 3[1930-(10.4\mathrm{n}\left)\right]=5000\\ \therefore \mathrm{n}=\frac{(5790-5000)}{3\times 10.4}=\frac{790}{31.2}=25\mathrm{\%}\end{array}$