Correct Answer - Option 4 :

\({2d_1d_2 \over d_1+d_2}\)
**CONCEPT**:

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

**mass = density × Volume**

**m = d × V**

**EXPLANATION**:

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

The density of first fluid = d_{1}

**Volume of first fluid = V**_{1} = m / d_{1} ................(i)

The density of second fluid = d2

**Volume of second fluid = V**_{2} = m / d**2** ................(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.**