In cell B1 of Worksheet B, enter this formula:

=SUMIF('Worksheet A'!A$1:A$100,A1,'Worksheet A'!B$1:B$100)

I've assumed you have 100 entries in worksheet A - adjust the cell
ranges as appropriate.

The formula can be copied down column B, to give you the totals from
sheet A against each ID number.

Hope this helps.

Pete