# How old is Bob?

Andrew Hamilton
Posers and Puzzles 21 Dec '08 18:56
1. 21 Dec '08 18:564 edits
Here is an extremely easy puzzle:

If Bob is currently twice the age of what Sue was when Sue was 8 years younger than the age Bob is now, then how old is Bob?

Ok -that was a bit too easy. But I vaguely reading a puzzle very much like this one above in a light-hearted book about relativity but I don’t remember exactly how it went but it was slightly more complicated than the above puzzle and it may have involved 3 people instead of 2 and, although the question still sounded amazingly simple, I just couldn’t work it out because it just sent my brain around in circles!
If anyone knows the puzzle I am referring to, please post it here ðŸ™‚
2. joe shmo
Strange Egg
21 Dec '08 23:30
Originally posted by Andrew Hamilton
Here is an extremely easy puzzle:

If Bob is currently twice the age of what Sue was when Sue was 8 years younger than the age Bob is now, then how old is Bob?

Ok -that was a bit too easy. But I vaguely reading a puzzle very much like this one above in a light-hearted book about relativity but I don’t remember exactly ...[text shortened]... y brain around in circles!
If anyone knows the puzzle I am referring to, please post it here ðŸ™‚
I get what you mean..I becomes a little confusing but I think I have it

let Sue age = x

Bob's age = 2x

Sues age is 8 years less than Bob's current age so

x = 2x-8

x=8

Bob is 2x so bob is 16
3. 22 Dec '08 00:53
This might be the one -- not sure but give it a try.

Bob and John form a team together. Bob is as old as John will be when Bob is twice as old as John was when Bob was half as old as the sum of their current ages. John is as old as Bob was when John was half as old as he will become over ten years.

How old are Bob and John?
4. 22 Dec '08 07:082 edits
Originally posted by ketch90
This might be the one -- not sure but give it a try.

Bob and John form a team together. Bob is as old as John will be when Bob is twice as old as John was when Bob was half as old as the sum of their current ages. John is as old as Bob was when John was half as old as he will become over ten years.

How old are Bob and John?
[when john was half as old as he will become over ten years] = [when john was 10]

so john is as old as Bob was when john was 10, from the second sentence.

let John(current) = x, and bob(current) = y. then x = |10+y-x| i think we can assume from the problem that bob is the older brother from the first sentence [Bob is as old as John will be ... ?] so since y > x, we know x = 10 + y - x. now note: y-x = x-10 (this will be useful later)

when bob was 1/2(x+y), john was [1/2(x+y) - (x-10)] years old. when bob is twice as big as that 2[1/2(x+y)-(x-10)], john will be 2[1/2(x+y)-(x-10)] - (x-10) years old. and this is bob's current age, according to the first sentence: so

y = 2[1/2(x+y)-(x-10)] - (x-10) = (x+y) - 2(x-10) - (x-10) = y -2x +30

or 0 = -2x +30 -> x=15. but then plugging that into the earlier equation x = 10 + y - x, we see that:

15 = 10+y - 15, or 30 = 10+y, or y = 20. thus john is 15 and bob is 20.

the key here is that the difference between their ages is constant, and relating everything to their current ages. then at its worst it's a system of two equations in two variables and can easily be solved.

good problem! cheers.
5. 22 Dec '08 09:33
Originally posted by joe shmo
I get what you mean..I becomes a little confusing but I think I have it

let Sue age = x

Bob's age = 2x

Sues age is 8 years less than Bob's current age so

x = 2x-8

x=8

Bob is 2x so bob is 16
Correct ðŸ™‚

…I becomes a little confusing but I think I have it.…

I know what you mean by ‘confusing’. It is amassing how the simplest question can confuse.

Note that it is impossible to determine Sue’s current age from this limited amount of information.
6. 22 Dec '08 09:43
Originally posted by Andrew Hamilton
Correct ðŸ™‚

[b]…I becomes a little confusing but I think I have it.…

I know what you mean by ‘confusing’. It is amassing how the simplest question can confuse.

Note that it is impossible to determine Sue’s current age from this limited amount of information.[/b]
nice! i actually didn't notice that on my first reading... Sue is irrelevant to the question really and it could be rephrased "how old am I if i'm now twice as old as I was 8 years ago" .. which is a rather simple question to answer, even without algebra.

but when you throw Sue into the mix it gets a bit more confusing ðŸ™‚
7. 22 Dec '08 09:595 edits
Originally posted by ketch90
This might be the one -- not sure but give it a try.

Bob and John form a team together. Bob is as old as John will be when Bob is twice as old as John was when Bob was half as old as the sum of their current ages. John is as old as Bob was when John was half as old as he will become over ten years.

How old are Bob and John?
…This might be the one -- not sure but give it a try.…

That’s good and you are vaguely on the right track but I forgot to mention that, although I cannot remember exactly what the original puzzle said, I distinctly remember that the original puzzle consisted of just TWO single whole sentences! -one stating the relationship between the ages of ~3 people (I think) followed by one that just asked “how old is X“ (where I don’t remember the name of “X“ ) -my apologies ðŸ™‚

Your puzzle consists of 3 sentences stating the relationship between the ages of 3 people followed by one that just asked “how old is Bob“ and has about twice the number of words than the original (I think) -good puzzle though.

I tried:

“Bob was twice the age of Sue when Jill was four years away from being half the age of Bob is now.
How old is Bob?”

-And for a while I thought that worked only to then realise that it is complete nonsense because the above has an infinite number of solutions!

But the original sounded something like the above and had about the same number of words and sounded astonishingly simple and yet had me completely go around in circles trying to work it out until I gave up!
The book even gave the answer on the next page and I still didn't get it (I no longer have that book and I don't remember its title).