What is the effective density of the mixture of water and milk when
i. they are taken with same masses ?

Explanation

Let us say the densities of water and milk are `rho_(1)andrho_(2).`
When they are taken with same mass 'm' and their volumes are `V_(1)andV_(2),` the mass of water `m=rho_(1)V_(1),V_(1)=(m)/(rho_(1))` and the mass of milk m = `rho_(2)V_(2),V_(2)=(m)/(rho_(2))`
Total mass of water and milk is m + m = 2m
Total volume of water and milk is `V_(1)+V_(2)=(m)/(rho_(1))+(m)/(rho_(2))=m((1)/(rho_(1))+(1)/(rho_(2)))=(m(rho_(1)+rho_(2)))/(rho_(1)rho_(2))`
The effective density of the mixture
`(rho_("eff"))=("Total mass")/("Total volume")=(2m)/(m(rho_(1)+rho_(2))//rho_(1)rho_(2))=(2)/((rho_(1)+rho_(2))rho_(1)rho_(2))=(2rho_(1)rho_(2))/(rho_(1)+rho_(2))`