A little teaser

[Ahmed]

Sharon is twice as old as Graham was when Sharon was as old as Graham is now.

If Graham is 24, how old is Sharon?

[badlad]

would that be 36

[Ahmed]

No, it's not 36

[bernardo]

32.

[Ahmed]

Correct bernardo. Well done.
How long did it take you to work it out?

[bernardo]

It more difficult than it sounds.  This is how I worked it out:



(1) Sh is twice as old as Gr was when Sh was as old as Gr is now

(2) Gr = 24



put (2) into (1) and you get



(3) Sh is twice as old as Gr was when Sh was 24



Let a = Sh now

Let b = Gr now

Let c = Sh then

Let d = Gr then



Therefore

(4) "Sh was as old as Gr is now" means b = c

(5) "Sh is twice as old as Gr was" means a = 2d

(6) constant age difference means that a - b = c - d

(7) Gr is now 24 means that b = c = 24



put (4) into (6) and you get

(8) a - b = b - d



put (5) into (8) and you get

(9) 2d - b = b - d



add d to both sides:

(10) 3d - b = b



add b to both sides:

(11) 3d = 2b



we know that b = 24, so:

3d = 48

d = 16

but b = c so therefore c = 24



constant age difference means that a = 32



So Shirley and Graham are now 32 and 24;

when Shirley was 24 they were 24 and 16.



QED

 

 

[badlad]

shame on me. I misread the question.

[bernardo]

About 2 or 3 minutes I think.  At first I thought it was easy and straightforward, but I had to resort to algebra instead of instinct.  It took 8 minutes to type out the explanation, and then I had to get rid of loads of coloured bits because the thingy said it was more than 2000 characters.  The gremlin has put in lots of extra spaces.

[badlad]

but who is Shirley ?

[Ahmed]

Well done bernardo.

But you forgot one thing...........The fomulae to change Sharon into Shirley ;-)

[bernardo]

It more difficult than it sounds.  This is how I worked it out:


(1) Sh is twice as old as Gr was when Sh was as old as Gr is now
(2) Gr = 24

put (2) into (1) and you get
(3) Sh is twice as old as Gr was when Sh was 24

Let a = Sh now
Let b = Gr now
Let c = Sh then
Let d = Gr then

Therefore
(4) "Sh was as old as Gr is now" means b = c
(5) "Sh is twice as old as Gr was" means a = 2d
(6) constant age difference means that a - b = c - d
(7) Gr is now 24 means that b = c = 24

put (4) into (6) and you get
(8) a - b = b - d


put (5) into (8) and you get
(9) 2d - b = b - d

add d to both sides:
(10) 3d - b = b

add b to both sides:
(11) 3d = 2b

we know that b = 24, so:

3d = 48
d = 16

but b = c so therefore c = 24

constant age difference means that a = 32

So Shirley and Graham are now 32 and 24;
when Shirley was 24 they were 24 and 16.



QED

[bernardo]

Shirley is Sharon's twin sister.

[badlad]

Nice one BERNARDO

[bernardo]

Before resorting to algebra, I tried out various obvious possibilities like 36, 48, 30, or even 24, but they all didn't work.  So I had to algebra instead.

[beachy]

32

[lats]

Well done beachy, good work, i am proud of you