Two substances of densities P1 and P2 are mixed in equal volume, and their relative density is 4 . When they are mixed in equal masses, relative density is 3 . The values of P1 and P2 respectively are;

Density is defined as mass per unit volume [1]. When two substances of densities P1 and P2 are mixed in equal volumes (V), the total mass is (P1V + P2V) and total volume is 2V. The mixture density is (P1 + P2) / 2. Given this equals 4, we get P1 + P2 = 8. When mixed in equal masses (M), the total mass is 2M and total volume is (M/P1 + M/P2). The mixture density is 2P1P2 / (P1 + P2). Given this equals 3, and substituting P1 + P2 = 8, we find 2P1P2 / 8 = 3, which simplifies to P1P2 = 12. We now have two equations: P1 + P2 = 8 and P1P2 = 12. Solving these quadratic roots or by inspection, the values are 6 and 2.

Sources

1. [1] Science ,Class VIII . NCERT(Revised ed 2025) > Chapter 9: The Amazing World of Solutes, Solvents, and Solutions > How do scientists define density? > p. 140