These are (emphasis by me):
Collisions of gas molecules are perfectly elastic. This means that total energy of molecules before and after the collision remains same. There may be exchange of energy between colliding molecules, their individual energies may change, but the sum of their energies remains constant. If there were loss of kinetic energy. the motion of molecules will stop and gases will settle down. This is contrary to what is actually observed.
At any particular time, different particles in the gas have different speeds and hence different kinetic energies. This assumption is reasonable because as the particles collide. we expect their speed to change. Even if initial speed of all the particles was same, the molecular collisions will disrupt this uniformity. Consequently. the particles must have different speeds. which go on changing constantly. It is possible to show that though the individual speeds are changing, the distribution of speeds remains constant at a particular temperature.
Now going along the line of the second statement (i.e.,assuming that initially all particles having the same speed initially) and making additional assumption that ideal gas has same kind of molecules we can show that (via conservation of kinetic energy and momentum) the speed of the particle before and after collision is the same.
So why this isn't the case for the statement in the book? Are there some other factors acting in there that change the situation?
Is the case (of same speed) possible for real gases? (Assuming that ideal one is possible)