Buying a rope
A man wants to buy a rope and so he goes into a shop. The shopman tells him that he has only ropes with a lengh of 100 feet for 20 cents each foot
The man tells him to cut off 20 feet of one 100-feet rope and sell it to him. The shopman measures the 20 feet with a 1 yard staff, but the man notes that the staff is 3 inches too short as it ends at the 33 inch mark.
After the shopman cut the rope off he said: „i changed my mind, I want to buy the 80 feet.“, so he gave him a 50 dollar note, but because the shopman couldn't change it he went to the neigbour shop to change the note and gave the change to the man, but he didn't knew, that the note was counterfeit so he had to displace it to the neigbour shop
So how many money did the shopman lost at all?
(sorry for my bad english)
posted by Carc at
7:10 AM
19 Comments:
It seems the shop owner lost:
(the 20ft. piece of cut rope, could still be sold, so that is
not a loss)
80Ft. @ $.20 = $16.00
$34.00 change from the purchase
$50.00 replacement to neighbor
Total - $100.00 loss
Problem: stated that the 20 ft. piece was measured with a 1 ft. staff, so the 3 inch shortage of the staff does not affect the measurement.
This post has been removed by the author.
Once the 20 ft. piece was measured with a 1 ft. staff (as stated), the rope remaining on the roll was 80 ft. and required no further measuring to make the sale. However, if the 80 ft sale rope was measured with the flawed staff(apparent 3" short yardstick), then the customer did not take 80 ft of rope. He actually took:
11 inches x 80 = 880 inches instead of
12 inches x 80 = 960 imches
So the actual loss of rope would be
73.3333 x .20 = $14.67
So measuring with the flawed yardstick, the loss would be:
$14.67 Rope
$34.00 Change
$50.00 Replacement of bogus bill
$98.67 Total loss
So, we need clarification as to whether the shop owner sold the acurately measured 80 ft. remaining on the roll from the first cut. or if he re-measured using the flawed yardstick.
Depends on how you determine the shopman's value. The shopman
would have been trying to measure of 6*36" + 24" = 20', but he
actually measured of 6*33"+24" = 18.5', leaving 81.5 feet. He gave
away 1.5', the value of which is $0.30, so that what he lost.
(I've assumed that you meant a 1 yard staff).
But, I think you might be saying that he had to make good the $50
with his neighbour, in which case he lost $50.30.
That just leaves the problem of 18.5' piece of rope. Is it worth
18.5 * $0.20 = $3.70 or is it sellable as 20'*$0.20 = $4.00?
Omitted one step above:
the 888 inches is 73.3333 ft.
x $.20 price per ft. = $14.67
1) The confusion about "1 foot staff" and "3 inches too short" makes me think the problem description was originally meant to use "yards", not "feet", throughout.
Hence the original rope was 100 yards, priced at 20 cents per yard; the man originally wanted 20 yards; the shopman measured 20 yards using a 33-inch yardstick; and the man paid for the 80-yard segment with a counterfeit bill.
2) Since the shopman measured the 20 yards using the short stick, not the 80 yards, the thief ends up with MORE than 80 yards, not less.
3) The short segment of rope measured, intended to be 20 yards (720 inches) is therefore only 18 2/3 yards (660 inches); the long segment is therefore 81 2/3 yards (245 feet).
4) The shopman lost:
* 81 2/3 yards of rope, priced at 20 cents per yard = $16.33
* Change from $50: the shopman thought he was giving change for 80 yards, which would have been worth $16.00, so he gave $34.00 change
* Replacement cost of the counterfeit note: $50
Total loss: $100.33
(In fact, the shopman lost nothing, because his insurance paid for it all)
He has lost $34 plus the value of the rope that the man bought with the fake $50 note.
There is some ambiguity in the question re the measuring of the rope, the questions states a 1 foot staff which ends at 33inches. Presumably this should read a 1 yard staff.
Assuming that it is a 1 yard staff then I would agree with Chris's analysis of the measurement of the rope and assume that he has given the man 81.5 feet of rope worth 81.5 x $0.20 = $16.30.
I would therefore agree with Chris in stating that he has lost total value of $34 + $16.30 = $50.30.
Zaux & Ross,
The shopkeeper hasn't lost $50 for replacing the fake note, because the neighbour gave him $50 worth of genuine currency when he changed it for him.
This $50 that the shopkeeper received for the fake note would have been returned to the neighbour, so the shopkeeper's net loss for the fake note is $0.
You have already accounted for the loss resulting from the fake note in the change and the value of the rope given to the man.
D'oh, I should have remembered that situation from the problem about the $27.
OK, but I stand by my assessment that our author meant "yards" everywhere he wrote "feet", so his loss is still $50.33, not $50.30.
Should we attempt to solve the problem based upon what we think was intended, or based upon actual wording. It seems the most loggical thing to do, is to solve based upon actual wording.
As for the %50 replacement:
C gives A a bogus $50 for mdse. and change.
A asks B for change for the bogus $50
At this point B is short $50.
B realizes the bill is bogus and ask A to replace it.
Now A is short $50 plus the mdse. and the change.
C has gained the mdse. plus the change for the bogus $50.
oops, sorry for that mistake, i meant a 1 yard staff(shame on you, you complicate english units!).
but this is the only one which has to be yard(sorry, ross :) ) and the right answer is $50.30
and about the neigbour:
it is absolutely irrelevant if the deal with the neigbour exist or not, because when the shopman changes the fake note with him he has a win of $50 (0$ worth of the fake one turns into real $50), but he has to pay back that amount, so the win/loose of the deal is all in all +- $0
Hey Zaux, your analysis of the exchange of the fake $50 is not correct.
A gets a fake $50
Changes with B who gives him $50 of genuine currency.
B realises the note is fake and asks for the money back in return for the fake note.
At the end of this neither is up nor down, the status quo is restored: A has the fake note back, B has his money back and has neither lost nor gained.
It would be exactly the same if the note was never exchanged with the neighbour at all. The exchange with the neighbour is an irrelevant red herring.
maybe feet refers to actual human feet?
hi Dual ...
what was I thinking ... you're right ... I obviously need more coffee :-)
When in doubt.... drink more coffee.
If it doesn't help, try vodka.
To answer the question with the actual loss, you need information that's not given. Needed to know is how much the shopkeeper PAID for the rope. That would be be his true loss, the other is unrealised eitherway. :)
Last Anonymous. The true value of the loss is far more complex to calculate than that. Storage costs (rent, rates etc.,) cost of re-ordering etc.
I'm gonna go with $51.
He measured of 20' with a yard stick that's 3" too short. 20' * 3" = 60" or 5' too short. meaning what was left was an 85' peice of rope.
He bought that 85' peice of rope for $16 (80' * .2 = $16) and got back $34 in change.
So, the shopkeeper has lost 85' (85' * .2 = $17) of rope and $34. Total of $51.
The exchange with the neighor is irrelevent.
However, you can argue, that he may eventually sell his leftover 15' rope labeled as a 20'. So he can recoupe $1 ('5 * .2 = $1). But the question seems to want the answer immediately following the bad transaction, not at the end of the fiscal period..
Hi EB. You goofed the length measurements. The ruler is 33" long but was (presumably) treated as if it were 36" long. 20' is 6*36" + 24". So was 6*3" = 1.5'short. That $0.30 value.
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