HOW OLD WAS MARY?
(
Money Puzzles)
Here is a funny little age problem, by the late Sam Loyd, which has been
very popular in the United States. Can you unravel the mystery?
The combined ages of Mary and Ann are forty-four years, and Mary is
twice as old as Ann was when Mary was half as old as Ann will be when
Ann is three times as old as Mary was when Mary was three times as old
as Ann. How old is Mary? That is all, but can you work it out? If not,
ask your friends to help you, and watch the shadow of bewilderment creep
over their faces as they attempt to grip the intricacies of the
question.
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 271/2 and Ann 161/2. 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 (271/2) twice as old as Ann
was (133/4) when Mary was half as old (243/4) as Ann will be (491/2) when Ann
is three times as old (491/2) as Mary was (161/2) when Mary was (161/2) three
times as old as Ann (51/2)." Now, check this backwards. When Mary was
three times as old as Ann, Mary was 161/2 and Ann 51/2 (11 years younger).
Then we get 491/2 for the age Ann will be when she is three times as old
as Mary was then. When Mary was half this she was 243/4. And at that time
Ann must have been 133/4 (11 years younger). Therefore Mary is now twice
as old--271/2, and Ann 11 years younger--161/2.
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