For any two people, the older of the two is twice the younger's age when the
younger is the same age the older was when the younger was born.

The mother was 27 when the daughter was born.  So last year the daughter was 27
and the mother was 54.  So this year the daughter is 28 and the mother is 55.

Or by algebra:

      M - 1 = 2D
          M = D + 27

 D + 27 + 1 = 2D
 
     D + 28 = 2D

         28 =  D

          M = 28 + 27

          M = 55 

Edwin