In making an alloy, a substance of specific gravity ${s_1}$ and mass ${m_1}$ is mixed with another substance of specific gravity ${s_2}$ and mass ${m_2}$; then the specific gravity of the alloy is
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(c)Specific gravity of alloy $ = \frac{{{\rm{Mass of alloy }}}}{{{\rm{Volume of alloy}} \times {\rm{density of water }}}}$
$ = \frac{{{m_1} + {m_2}}}{{\left( {\frac{{{m_1}}}{{{\rho _1}}} + \frac{{{m_2}}}{{{\rho _2}}}} \right) \times {\rho _w}}}$$ = \frac{{{m_1} + {m_2}}}{{\frac{{{m_1}}}{{{\rho _1}/{\rho _w}}} + \frac{{{m_2}}}{{{\rho _2}/{\rho _w}}}}} = \frac{{{m_1} + {m_2}}}{{\frac{{{m_1}}}{{{s_1}}} + \frac{{{m_2}}}{{{s_2}}}}}$ $\left[ {{\rm{As\, specific \,gravity \,of\,substance }} = \frac{{{\rm{density \,of\, substance }}}}{{{\rm{density\, of \,water}}}}} \right]$
$ = \frac{{{m_1} + {m_2}}}{{\left( {\frac{{{m_1}}}{{{\rho _1}}} + \frac{{{m_2}}}{{{\rho _2}}}} \right) \times {\rho _w}}}$$ = \frac{{{m_1} + {m_2}}}{{\frac{{{m_1}}}{{{\rho _1}/{\rho _w}}} + \frac{{{m_2}}}{{{\rho _2}/{\rho _w}}}}} = \frac{{{m_1} + {m_2}}}{{\frac{{{m_1}}}{{{s_1}}} + \frac{{{m_2}}}{{{s_2}}}}}$ $\left[ {{\rm{As\, specific \,gravity \,of\,substance }} = \frac{{{\rm{density \,of\, substance }}}}{{{\rm{density\, of \,water}}}}} \right]$
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