Question

Equal masses of water and a liquid of relative density 2 are mixed together. Then, the mixture has a relative density of:

• A. $\frac{4}{3}$
• B. $\frac{2}{3}$
• C. $\frac{4}{5}$
• D. $\frac{4}{6}$

Answer 1

The correct option is A $\frac{4}{3}$

The masses of two liquids are equal, let it be m.
Let the relative densities of water and liquid be ρ1 and ρ2 respectively.
The volume of the water and liquid be v1 and v2 respectively.
The volume of the mixture would be, v = v1 + v2 ................(1)
Also, $volume=\frac{mass}{density}$
Thus,$v=\frac{2m}{\rho }$ ...............(2)
Also from (1), $v=\frac{m}{{\rho }_1}+\frac{m}{{\rho }_2}$ ...............(3)
Here, ${\rho }_1=1,{\rho }_2=2$ and ρ is the relative density of the mixture.
Now equating (2) and (3) , $\frac{2}{\rho }=\frac{1}{{\rho }_1}+\frac{1}{{\rho }_2}$
By substituting the values, we get, $\frac{\rho }{2}=\frac{2}{3}$
The relative density of the combined liquid will be, $\rho =\frac{4}{3}$.