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Find density of mixture if the same mass of two fluids are mixed together. (densities of both the fluids are d1 and d2 )
1. \({d_1+d_2 \over 2}\)
2. \(\sqrt{d_1d_2 }\)
3. \({1 \over d_1}+{1 \over d_2}\)
4. \({2d_1d_2 \over d_1+d_2}\)

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Correct Answer - Option 4 : \({2d_1d_2 \over d_1+d_2}\)


  • The relation between mass, density, and volume is given by:

mass = density × Volume

m = d × V


Given that both the fluids have the same mass. Let it is m.

The density of first fluid = d1

Volume of first fluid = V1 = m / d1 ................(i)

The density of second fluid = d2

Volume of second fluid = V2 = m / d2 ................(ii)

Now after mixing the fluids.

\(Density ~of~ mixture = {Total~mass \over Total ~volume}\)

\(Density ~of~ mixture = {m+m \over V_1+ V_2}\)

From eq (i) and (ii)

\(Density ~of~ mixture = {2m \over {m \over d_1}+ {m \over d_2}}\)

\(Density ~of~ mixture = {2 \over {1 \over d_1} + {1 \over d_2}}\)

\(Density ~of~ mixture = {2 d_1 d_2 \over {d_1 + d_2}}\)

So the correct answer is option 4.

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