Duplicate values in a column in pandas

Question

I have an input data like:

Customer bill
Alex      20
lily      50
harris    30
johny     90
Alex      35
lily      25

I want an input data like:

Customer bill
Alex      55
lily      75
harris    30
johny     90

i.e. to find the duplicates in a column, and mathematical operations in other column. The data has 10000 entry, please help.