Question

In an inelastic collision between two bodies, the physical quantity that is conserved

Answer 1

During a collision, the forces on the colliding bodies are always equal and opposite at each instant. Conservation of momentum is nothing but Newton's second law. Hence the Impulses on each body are equal and opposite for the entire time of the collision. Hence the change in momentum of one body is compensated by other bodies in relation to the current body or simply to say by all the other bodies in the system.