Can you solve this puzzle (derived from a Monty Python sketch)?

Question

John said to Bob, “You are such an exaggerator. Every time you say a number it’s 2 times the real value.” Bob replied, “You’re a worse underestimater. Every time you say a number we need to multiply it by 50.” If John says that a mattress costs 40 dollars, how much would Bob say it costs, and how much does it really cost?
(With regards to Monty Python's Flying Circus episode 8)

For all of you who have answered so far:
If bob is an exaggerator, how can the real cost be higher than his?

bandf
You are correct. Their statements contain numbers, and therefore these numbers too are exaggerated or understated.

After 12 responses no one is correct.

And yes, I know the answer. (I created the puzzle). If I dont get a correct response i will publish it.

Answer 1

Don't forget that they underestimate and exaggerate every number, so even their original statements are affected. When John says, "Every time you say a number it's *2* times the real value" he is underestimating. And when Bob replies "Every time you say a number we need to multiply it by *50*" he is exaggerating. We first have to figure out what their actual underestimating and exaggeration factors are:

Let's take John's underestimating factor to be J. So when he says, "2 times", he is underestimating by J. So Bob's real exaggeration factor of B is 2*J.

Similarly, Bob's statement about J being 50 is 2*J too much. The real value is 50/2*J.

So we have John's underestimating factor is both J and 50/2*J.

Equating these two we have:
J = 50/2*J

Multiply both sides by J:
J^2 = 50/2
J^2 = 25

Take the square root of both sides:
J = +/-5 (let's ignore -5 as a possible answer and just say J = 5)
J = 5

Now figure out B:
B = 2J
J = 5, so 2J = 10
B = 10

So everything John says needs to be *multiplied* by 5 and everything Bob says needs to be *divided* by 10.

Now we can get back to the original question.

If John says the mattress cost $40, it really costs 5 times this or $200 dollars. Bob, on the other hand, over estimates by a factor of 10, so he would say it was actually $2000.

The answer are:
The mattress really costs $200
John underestimates by a factor of 5 and says it is only $40.
Bob overestimates by a factor of 10 and says it is $2000.

Answer 2

You need to divide Bob's numbers by 10 and multiply John's numbers by 5. Thus when John said to Bob, “You are such an exaggerator. Every time you say a number it’s 2 times the real value.” you really need to divide his numbers by 2*5=10.

When Bob replied, “You’re a worse underestimater. Every time you say a number we need to multiply it by 50.”, you really need to multiply John's number by 50/10=5 (thus the claim is valid).

Thus, when John says a mattress costs 40 dollars, it really cost 5*40=200 dollars. Thus Bob would say that it costs 200*10=2000 dollars.

There actually is another possible answer though: It is possible that John says the mattress costs 40 dollars, Bob says the mattress costs 2000 dollars, but in reality they were paid 200 dollars to take the mattress (in other words, the ma tress actually costs -200 dollars).

This is possible if you need to multiply John's numbers by -5 and Bob's divided by -10.

It works just like before:

2*(-5)=-10

and

50/(-10)=-5

But I'm sure that wasn't the answer you were looking for :)

Answer 3

When John says the mattress costs 40 Dollars, the actual cost is 40*50 = 2000.

Bob would have said the mattress would have costed him 4000 dollars.

Answer 4

I'm working on it assuming that the numbers in the problem are also skewed, but it looks like there's a fundamental flaw in the problem. I'm going to write a program to see if it stabilizes and I'll be back in a bit.

Edit: The program broke down after 17 iterations and started returning infinity for both of them. This means that either there is an inherent flaw in the problem or I don't know the math necessary to properly analyze the problem.

Edit #2: Do you know the answer?

Edit #3: Or maybe I'm just stupid and made it more complicated than it really was.

Answer 5

Bob would say it cost $1000 while the real price would be $2000

Answer 6

bobs price would be 2000, johns price is 40, and the real price would be 20
50x40=2000, john is 2 times higher so divide johns price by 2 to get the price 40/2 =20

Answer 7

Bob would say 4000. The real amount is 2000.

Answer 8

the mattress $2000 and Bob would say it costs $4000

Answer 9

Real cost $2000.

Bob would say $1000.

Answer 10

Bob = 50 * 40 = $2,000
Actual: @000/2 = $1,000