The age of Mary to that of Ann must be as 5 to 3. And as the sum of
their ages was 44, Mary was 27½ and Ann 16½. One is exactly 11 years
older than the other. I will now insert in brackets in the original
statement the various ages specified: "Mary is (27½) twice as old as Ann
was (13¾) when Mary was half as old (24¾) as Ann will be (49½) when Ann
is three times as old (49½) as Mary was (16½) when Mary was (16½) three
times as old as Ann (5½)." Now, check this backwards. When Mary was
three times as old as Ann, Mary was 16½ and Ann 5½ (11 years younger).
Then we get 49½ for the age Ann will be when she is three times as old
as Mary was then. When Mary was half this she was 24¾. And at that time
Ann must have been 13¾ (11 years younger). Therefore Mary is now twice
as old--27½, and Ann 11 years younger--16½.