Initial amount of money: $800
After paying the cab driver $20 ; money = $800 - $20 = $780
Giving his mother 1/3 of the remaining amount, leaving him with 2/3 of it.
money = ($780) x (2/3) = $520
Giving his aunt 1/4 of the remaining amount, leaving him with 3/4 of it.
money = ($520)(3/4) = $390
Giving his friend 1/6 of the remaining amount, leaving him with 5/6 of it.
money = ($390)(5/6) = $325
Therefore, the amount of money Bob gets to keep is equal to $325.