CDS 2018 PYQ with Answer — If two miscible liquids of same volume but different densities P₁ and…

2018 · Q8

If two miscible liquids of same volume but different densities P₁ and P₂ are mixed, then the density of the mixture is given by

General KnowledgePhysics

A(P₁ + P₂)/2
B2P₁P₂/(P₁ + P₂)
C2P₁P₂/(P₁ − P₂)
DP₁P₂/(P₁ + P₂)

Explanation

Let each liquid have volume V. The total mass is P1*V + P2*V and the total volume is 2V. The mixture density is therefore (P1*V + P2*V) / (2V) = (P1 + P2)/2, the simple arithmetic mean of the two densities. The harmonic-mean form 2P1P2/(P1+P2) would apply if equal masses (not equal volumes) were mixed. Since the volumes are equal, the correct expression is (P1 + P2)/2.