A family of Microsoft spreadsheet software with tools for analyzing, charting, and communicating data.
Instead of deleting sheets, MOVE sheets to be deleted to a new workbook.
In the moved sheet workbook select all the sheets to be deleted and press CTRL+A and now press delete button. Don't delete the sheets.
Now in your original file, when you go to Data/Edit link you will find links to the file where sheets have been moved. select file there and break links.
You will not find any reference error now.
Please note to make your file more automated and efficient working you should change your original formula (=Bangalore!B3+Delhi!B3+...............Mumbai!B3) to
=SUM(Start:End!B3)
where Start and End are the first and last sheets. There may be any number of sheets in between and now even you delete a sheet you will not get #ref errors.