If two liquids of same masses but densities  ρ1 and  ρ2 respectively are mixed, then density of mixture is given by

The density of a mixture of two liquids with the same mass but different densities (ρ1 and ρ2) can be calculated using the formula for the density of a mixture, which is the total mass of the mixture divided by the total volume of the mixture.

Step 1: Calculate the total mass of the mixture. Since the two liquids have the same mass, you can simply double the mass of one of the liquids to get the total mass. Let's denote the mass of each liquid as m. So, the total mass M = m + m = 2m.

Step 2: Calculate the total volume of the mixture. The volume of each liquid can be calculated by dividing its mass by its density (V = m/ρ). So, the volume of the first liquid V1 = m/ρ1 and the volume of the second liquid V2 = m/ρ2. The total volume V = V1 + V2 = m/ρ1 + m/ρ2.

Step 3: Substitute the total mass and total volume into the formula for density. The density ρ of the mixture is given by ρ = M/V = 2m / (m/ρ1 + m/ρ2).

Step 4: Simplify the equation. The m in the numerator and denominator will cancel out, leaving ρ = 2 / (1/ρ1 + 1/ρ2).

So, the density of the mixture of two liquids with the same mass but different densities is given by ρ = 2 / (1/ρ1 + 1/ρ2).