How much the shopkeeper loses?

Question

I struck with this tricky math question

A girl went to a shop and bought a Rs.$200$ show piece. She gave a Rs.$1000$ note to shopkeeper. Shopkeeper didn't have any change so he went outside and took loan of Rs.$800$ from other shop and gave it to the girl. After sometime he realized that the Rs.$1000$ note was fake. So how much the shopkeeper loses?

Rs is Indian currency.

I think that the shopkeeper loses

the show piece price $200$ + he borrowed $800$ + fake note of $1000$ = Rs.$2000$

Am I right?

But he didn't give the 1000 note to other shopkeeper from where he borrowed. — Anirban Nag 'tintinmj', Mar 01 '14 at 05:51
It doesn't matter. He borrowed 800, and lost 200 worth of merchandise which is 800+200=1000 — homegrown, Mar 01 '14 at 05:54
To put it mathematically: $-800-200+0=-1000$. The $+0$ part is because the 1000 note was fake, and he did not gain anything from the transaction, he only lost. — homegrown, Mar 01 '14 at 05:58
Also, he did not lose 200 for the show piece, that's the retail price. Presumably he paid less for it, perhaps 150. — vadim123, Mar 01 '14 at 06:11
@vadim123: but he has lost the opportunity to sell the show piece for a profit, which is worth something. — , Mar 01 '14 at 06:48

score 0 · Answer 1 · answered Mar 01 '14 at 06:24

0

He would Lose $$$200 for the show piece because he was expecting to get 200 from it in revenue but now he would Take as a loss because he did not get the expected sale

$800 for the loan

answered Mar 01 '14 at 06:24

user126885

159

score 0 · Answer 2 · 2014-03-01T06:55:54.857

He lost 1000 Rs relative to what he expected: the only difference between his expectations and reality is that the note turns out to be worth 0 Rs rather than 1000 Rs.

The difference between reality and expectations is almost surely what the puzzle intends. If you think the puzzle is about the difference between what he started with and what he finished with, then:

He is down one show piece
He is down one loan for 1000 Rs
He is up one fake 1000 Rs note
He is up 200 Rs

and possibly other things (e.g. he is up "ability to visually recognize a thief" which may have some value if he can get help from the police).

Simplistically assigning monetary value to each of these things also tallies to -1000 Rs, although reality may be somewhat different.

It may also help to reorganize your view on the problem. The girl and shopkeeper underwent two separate transactions:

The shopkeeper gave 1000 Rs change for a fake 1000 Rs note
The shopkeeper and the girl underwent an exchange of the show piece for 200 Rs.

How much the shopkeeper loses?

2 Answers2