Question

An alloy of copper and zinc weighs 320 g in water and 302 g in a liquid of density 1.4 g/cm ³. If the density of copper is 8.9 g/cm ³ and that of zinc is 7.4 g/cm ³, find the measure of the masses of copper and zinc in the alloy.

Answer 1

$$\begin{gathered} Letthemassesofcopperandzincinthealloybe{m}_{2}and{m}_2. \\ totalmassofthealloy=m_1+m_2 \\ Thevolumeofthealloy=\frac{m_1}{8.9}+\frac{m_2}{7.4} \\ Thevolumeofthewaterdisplaced=\left(\frac{m_1}{8.9}+\frac{m_2}{7.4}\right). \\ Themassofthewaterdisplaced=volumeofwaterdisplaced\times densityofwater. \\ =\left(\frac{m_1}{8.9}+\frac{m_2}{7.4}\right)\times 1=\left(\frac{m_1}{8.9}+\frac{m_2}{7.4}\right). \\ Thusreducedmassofalloyinwater=\left(m_1+m_2\right)-\left(\frac{m_1}{8.9}+\frac{m_2}{7.4}\right)=320-----\left(1\right) \\ Similarlythereducedmassofalloyintheliquid=\left(m_1+m_2\right)-\left(\frac{m_1}{8.9}+\frac{m_2}{7.4}\right)\times 1.4=302-----\left(2\right) \\ Subtractingeqn\left(2\right)fromeqn\left(1\right),weget, \\ \left(\frac{m_1}{8.9}+\frac{m_2}{7.4}\right)\times 0.4=18 \\ or\left(\frac{m_1}{8.9}+\frac{m_2}{7.4}\right)=45----\left(3\right) \\ Puttingthisvalueof\left(\frac{m_1}{8.9}+\frac{m_2}{7.4}\right)ofineqn\left(1\right),weget, \\ {m}_1+m_2=320+45=365-----\left(4\right) \\ Nowfromeqns\left(3\right)and\left(4\right),weget, \\ {m}_1=189.87gand{m}_2=17513g. \end{gathered}$$