Question

22. Two identical containers have liquids of different
densities d1, and d2, but they weigh the same when
kept on a weighing pan. The density of the mixture
when they are mixed together will be​

Answer 1

Explanation:

V1=m /d1 and V2 = m/d2

V1+V2 =m / d1 + m / d2

D = (V1+V2)÷2m = m(1/d1+1/d2)/2m = (d1+d2)/2d1.d2

Answer 2

Solution:

let, v1 be the volume of the liquid with density d1 and

     v2 be the volume of the liquid with density d2.

as given in the question that the mass of both liquids with densities d1 and d2 are same.

so, let, m be the mass of both the liquids with densities d1 and d2.

as we know the formula of density that

density = mass/ volume

now,  d1 = m/v1

         v1 = m/d1   ------1

and  d2 = m/v2

        v2 = m/d2   ------2

after mixing both the liquid

mass, M = m +m = 2m

volume, V = v1+ v2 = m/d1+m/d2   from equation 1 and 2

             V = m(1/d1+1/d2)

density, D = M/V

   D = 2m/m(1/d1+1/d2)

   D = 2/(1/d1+1/d2)