I came to know the battery can be charged & discharged simultaneously like in
telephone exchanges.

But how is this possible. Current can either go inside or out of battery at a time.

 

I came to know the battery can be charged & discharged simultaneously like in
telephone exchanges.

But how is this possible. Current can either go inside or out of battery at a time.

Your second statement is quite true. So you have a contradiction between your two statements, which means your statement about a battery being charged and discharged at the same time cannot be true.

A battery has three current flow states of either charging, discharging, or having no current flow (idle). It can only do one at a time. It just depends upon whether the charging current is more than, less than, or equal to the load current.