Hey this is Presh Talwalkar. I received this
problem by email because it's going
viral on Facebook with thousands of
people arguing about the correct answer.
How smart are you? A guy walks into a
store and steals a hundred-dollar bill
from the register without the owner's
knowledge. He then buys seventy dollars
worth of good using the hundred-dollar
bill and the owner gives thirty dollars
in change. How much money did the owner lose?
Was it $30, $70, $100, $130, $170, or $200?
Can you figure it out?
Give this problem a try and when you're
ready keep watching the video for the correct answer.
In some math problems,
and in this story,
it helps to break the problem down into
different parts so at first we'll only
consider the first part of the story.
A guy walks into a store and steals a
hundred-dollar bill from the register
without the owner's knowledge.
At this point how much does the owner lose?
Everyone agrees the owner loses a hundred dollars.
The owner is at minus 100 from the initial
part of the story. So now let's
separately consider just the second
part of the story.
Imagine someone buys seventy dollars worth
of goods using a hundred-dollar bill and
the owner gives thirty dollars in change.
How much would you say the owner has
lost in just this part of the story?
Well if someone buys seventy dollars worth
of good using a hundred-dollar bill you
would expect the owner to give thirty
dollars in change. In fact the owner is
overseeing this transaction. So the owner
here is not losing any money.
The owner is you could say zero in this transaction.
So now we put these two
stories together
the total loss will be the sum of these
two parts of the story so we can add
-100 and 0 to get the total loss is
$100 the owner is negative one hundred
dollars from before the story started
the correct answer is the owner lost $100.
Now there's one technicality if you
want to really overthink this problem
and go into the accounting details.
Now when someone buys seventy dollars worth of
goods in a store it's not because the
goods are worth seventy dollars to the owner.
What happens here is the owner is
getting a hundred-dollar bill and gives
back thirty dollars in change but the
goods have some value V. This is usually
going to be less than seventy dollars so
you could say the owner's actually losing
the value of the goods but then getting
a net seventy dollars because it's a
hundred-dollar bill minus thirty dollars
in change but here the owner loses V
minus 70 or you could say the owner is
70 minus V in terms of the cash position
so if you were to take these two stories
now you add up the result the owner
ultimately loses thirty dollars plus the
value V of the goods
so if we assume the value V is seventy
dollars which you say seventy dollars
worth of goods then you would say the
owner lost a hundred dollars. So you can
still arrive at the same answer of a hundred
dollars but this is a little more
accurate in terms of pure accounting.
So why are so many people getting this
problem wrong?
Well one of the common answers is there
is a two-hundred-dollar loss to the
owner. Many people think this is because
in the first part of the story the owner
loses a hundred dollars that's stolen and
then in the second part of the story the
owner loses another hundred dollars
because the owner is giving up seventy
dollars worth of goods and thirty dollars
in change. So the mistake here is that it's
not taking into account the owner is
also getting a hundred-dollar bill so
when you take that other part of the
story where you get the hundred-dollar bill
that will adjust the total by +100 and when
you do that, that means the owner
ultimately lost a hundred dollars in total.
Another common answer is that the owner
had a $130 loss. This is
from the stolen hundred-dollar bill
and the thirty dollars in change.
Well the problem with this answer is
it's not taking into account that the owner
also gave up seventy dollars in goods
but also got a hundred-dollar bill so
when you take into account these
transactions the net result would be the
owner losing $100 which is
negative 100. So to summarize most of the
incorrect responses either didn't add or
subtract numbers correctly or they
didn't take into account every
transaction. It seems the fact that in
the second half of the story that person
used the stolen dollar bill somehow
people don't treat that as a genuine hundred-dollar bill.
That is a hundred dollars that the owner's getting back.
So when you take into account every single
transaction and you treated correctly as
either a loss or gain for the owner you
end up that the owner lost a hundred dollars.
Did you figure it out? Thanks for
watching this video please subscribe to
my channel i make videos on math and game
theory you can catch me on my blog
Mind Your Decisions you can follow on
facebook google+ and patreon you can
catch me on social media @preshtalwalkar
if you like this video please check out my
books there are links in the description.