Why conductivity of electrolyte decreases on dilution, but molar conductivity increases?
I've just been doing an experiment on this, and my understanding's not that great, but as I understand it the conductivity decreases because you have a lower concentration of charge carriers in the solution. The molar conductivity increases however, because as the charged ions get further apart they interact and slow each other down less. Essentially each ion becomes more able to move through the solution, but the increase in conductivity from this effect is outweighed by the decrease due to there being fewer ions in a given volume.

Personally I find it easier to think about the other way around. As you increase the concentration of the solution you get more charge carrying ions, so the conductivity increases. But because the ions get closer together they begin to interact and slow each other down so the conductivity per mole of the ions is reduced.

I hope you still find this useful and that I managed to explain what I meant