Let's call the original amount of Pavati's rent "x". If the rent increased by 5%, the new rent is 1.05x, which is the original rent plus a 5% increase. We know that the increase was $82, so we can set up the equation:
1.05x - x = 82
Simplifying the left side, we get:
0.05x = 82
Dividing both sides by 0.05, we get:
x = 1640
Therefore, the original amount of Pavati's rent was $1640.