perplexus.info :: Numbers : Age Difference

Age Difference (Posted on 2003-03-02)

Said Albert to Bertrand, "The last time we met, our ages were both prime numbers, and when I was a quarter of the age I am now, you were that age plus half the age your father would have been thirty years previous to when he was six times the age you would have been when I was half your age".

How old were Albert and Bertrand the last time they met?

Submitted by Ravi Raja

Rating: 3.5556 (9 votes)

Solution: (Hide)

Albert and Bertrand were 2 and 5 years old repectively the last time they met.
If A and B are Albert's and Bertrand's present ages and a and b are their ages when Albert was half Bertrand's age then
B - 3A/4 = (A/4) + (6b - 30)/2
Since their ages have always had the same difference we have
B - A = 3b - 15 = b - a
and since 2a = b then a = 3 and b = 6.
So their ages differ by 3. Since all primes except 2 are odd and differ by an even number we can only have 2 and 5, Bertrand being the older of the two.

Comments: ( You must be logged in to post comments.)

Subject	Author	Date
explanation to puzzle answer	K Sengupta	2022-07-07 00:27:10
re: the text vs reason	Ady TZIDON	2014-11-25 17:23:12
re: the text vs reason	Ady TZIDON	2014-11-25 17:23:12
answer	K Sengupta	2007-11-29 05:01:23
re: Solution attempt	x	2003-04-29 00:14:06
Solution attempt	DJ	2003-03-03 15:53:24
Solution	Charlie	2003-03-02 10:15:14

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