Expert: David Hemmer - 8/6/2007

Question
Hey David, this is more of a riddle than a math problem (even though it deals with math).  I thought maybe you could help me out with this.

I have a problem that has been bothering me for a while.  I got a Mensa: Brain Bafflers book and I have solved most of them.  However, there is this one riddle which I am confused about.  It's pretty simple but yet the book gives a totally different answer that I can't understand how they got that answer.

The riddle is this,

Jim is 36 years old.  He is twice as old as Sid was when he, Jim, was as old as Sid is now.  How old was Sid a year ago.  

Well, my answer is 23.  However the books answer is 18.  If Sid were 24 now, that means when Jim was 24, Sid was (36-24=12) 12 years old.

Am I missing something here or is the book wrong?

Answer
Assuming you have typed the puzzle exactly as written then your answer is wrong.

According to you, right now Jim is 36 and Sid is 24. At the time Jim was 24, Sid was 12. Thus the riddle would read that "Jim is twice as old as 12" which is wrong.

Let's let X be Sid's current age. Then the riddle says that Sid was 18 when Jim was X. This occurred 36-X years ago. Thus we have:

18=X-(36-X)

18=2X-36.

X=27
So Sid is currently 27 and Jim is 36. When Jim was 27 then Sid was 18, as required. Then the final answer is 26.