When equal volumes of two metals are mixed together the specific gravity of alloy is 4. When equal masses of the same two metals are mixed together the specific gravity of the alloy becomes 3. find specific gravity of each metal?
(specific gravity `=("density of substance")/("density of water"))`

Explanation

Let `m_(1),m_(2)` be the mass of two metals and `V_(1)` , `V_(2)` be their volumes .
Density of the mixture of two metal is
`rho = (m_(1)+m_(2))/(V_(1)+V_(2))`
When equal volume of two metals are mixed, then `V_(1)=V_(2) + V(say)`. Let `rho_(1)` and `rho_(2)` be the densities of two metals, so
`m_(1)=rho_(1) V_(1) = rho_(1)V` and `m_(2) = rho_(2)V_(2)=rho_(2)V`
`rho (rho_(1)V+rho_(2)V)/(V+V) = (rho_(1)rho_(2))/(2)`
or `rho_(1)+rho_(2) = 2rho = 2 xx 4 = 8`...(i)
When equal masses of two metals are mixed, then
`m_(1)=m_(2) = m (say)`
Now `V_(1) = m//rho_(1)` and `V_(2) = m//rho_(2)`
so `rho = (m+m)/(m//rho_(1)+m//rho_(2)) = (2rho_(1)rho_(2))/(rho_(1)+rho_(2)) = 3`
or `rho_(1)rho_(2) = 3/2 (rho_(1)+rho_(2)) = 3/2 xx 8 = 12` ...(ii)
Solving (i) and (ii), we get : `rho_(1) = 2 and rho_(2) = 6`
The specific gravity of two metals are 2 and 6 respectively.