How Old
Is Mary?
.
Answer :
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.

