Question Summary:
How is it to pray salah behind someone who works in the bank?

Question Detail:

Is it permissible to offer salah behind a person who works in non Islamic bank.If  no then what about us who in one or the other way are part of banking system be it in the form of bank accounts with money or govt provident fund which is subjected to interest

Answer :

In the Name of Allah, the Most Gracious, the Most Merciful.
As-salāmu ‘alaykum wa-rahmatullāhi wa-barakātuh.
We understand from your query that you are not referring to a person appointed as a regular imam in a masjid.
If some working class people perform salah by themselves, and if one person is required to lead the salah, if he is involved in some sinful act, for example dealing in interest act, he should decline being an imam. This is a self-conscious (diyanat) decision one has to make. In principle, the Imamat of a faasiq is makrooh. [1]
A faasiq is defined as that person who is engaged in some major sin as explained above. [2]
If a person is unsure of the nature of his act, for example working in a bank, he should enquire from the Ulama. Whilst some of the employment activities of a conventional bank is prohibited, that is not so for all forms of employment in a conventional bank. [3]
In any event, if a person involved in some sinful activity performs/leads salah, the salah will be valid.[4]
 
And Allah Ta’āla Knows Best
Zakariya Memon
Student Darul Iftaa
Chatham, Canada 
Checked and Approved by,
Mufti Ebrahim Desai.
Daruliftaa.net