A man is 6 years older than his spouse.
Four years ago he had been married to her exactly half of his life and 10 years from now she will have been married to him for two thirds of her life.
What will be the man's age on their 50th anniversary (provided they both survive)?

Let M be the man's age at marriage and N be his age now.

Four years ago he was N - 4, which was twice his age at marriage:

N - 4 = 2M

N = 2M + 4

In 10 years, the couple will have been married N + 10 - M years, and the wife will be N + 10 - 6:

N + 10 - M = 2(N + 10 - 6) / 3

M + 14 = 2(2M + 8) / 3

3M + 42 = 4M + 16

M = 42 - 16 = 26

So the man was married at age 26 and will be 76 on his 50th anniversary.

Posted by Charlie on 2011-05-23 13:59:11