Question

When equal volume of 2 liquid are mixed the specific gravity of mixture is 7 by 2 when equal masses of the same to liquid mixed the specific gravity is 12 by 7 find the specific gravity of 2 liquid

Answer 1

Let ρ​1 and ρ​2 be the densities of two liquids.

When equal volumes of two liquids are mixed, then special gravity (ρ) is given by

ρ=(ρ1+ρ2)/2
Here, ρ1 and ρ2 are the densities of two liquid.
7/2=(ρ1+ρ2)/2
⇒ρ1+ρ2=7 .....(1)

When equal masses of the same two liquids are mixed, then ​special gravity (ρ) is given by

ρ=2ρ1ρ2/(ρ1+ρ2)
⇒12/7=2ρ1ρ2/(ρ1+ρ2)
⇒6ρ1+6ρ2=7ρ1ρ2 .....(2)

Solving equation (1) and (2), we have
ρ1=6 kg m^−3 and
ρ2= 1 kg m^−3