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# Find the length of the metre scale

Posted on 2004-04-16
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a cloth merchant uses a metre scale with which he makes a profit of 40%.By  using a improper metre scale,he makes a profit of 39%.What is his length of the metre scale?
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Expert Comment

ID: 10840617
With a correct metre scale, P (price) = 0.4 + 0.6 for one metre (0.4 profit).
If profit is only 0.39,  P1metre = 0.39+0.60 = 0.99 => "1 metre" = 1 / 0.99 = 1.01 exact metre.
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Author Comment

ID: 10840904
what i did(i am not sure whether it is correct or not)

metre     profit
100        140
?            139

=(100*139)/140=99.28metre

Is this right or wrong?
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Expert Comment

ID: 10841493
WRONG

Without any mathematics at all.

If he is making LESS profit, he must be selling MORE cloth, not less.

Furtive Bertie.
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Expert Comment

ID: 10841834
SCALE 1
length = 1M
cost = c
Profit = .4
Price P = (c*140)/100 = c * 1.4

SCALE 2
length = L
cost = L * c
Profit = .39
Price = P  - SAME PRICE AS SCALE 1

PROFIT = (PRICE - cost)/cost

so we get the equations:

0.39 = ((c*1.4) - Lc)/Lc

c cancels,
0.39 = (1.4 - L) /L

solving for L gives L = 1.4/1.39 = 1.0071942446 and a bit!

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Expert Comment

ID: 10841844
Erm, is this homework?
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Expert Comment

ID: 10841863
And that answer is in metres.

I think you just have your sum the wrong way up

:-)
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LVL 10

Expert Comment

ID: 10842321
My understanding of the problem is
1. profit 40% : that means that for a 100% price, seller profit is 40%, cost of cloth is 60% (rest)
2. he makes 39% though : as I stated in my first answer, the seller thinks he has a 1 meter scale,
why it is not.
What can it be ? If the scale is *smaller* than an actual meter,
a) - he will sell 1 meter to a client, being actually less, e.g. the scale is 0.90m => he sells 0.90m of cloth for the price of 1.00,
as you understand, in this case, he makes more profit since he gets the money for 1 m while it is only 0.90m cloth...
b) - in our problem (I gave the solution before thinking you know it :) this is the opposite:
=> the seller thinks he has a 1m scale and sells 1m of his scale to a client
=> he thinks he makes 40% profit, while actually it is only 39% ...
=> so that means this is the opposite of a) : he gives more cloth than 1 actual meter.
why ? because he takes measure with a wrong scale being  bigger than 1 meter.
Well, you have already the math in the 1st answer, but try to think by yourself:
40% of 100% is actually 39%, so 39% margin (profit) + the previous 60% is only 99%...
What could be the scale making only 99% while you were supposed to have 100% = 1.00m ?
[try not to look at my solution again, try by yourself first]
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Expert Comment

ID: 10843558
Mercantilum:
He makes 40% profit.  This does NOT mean that 40/100 is profit.
He makes 40% on the COST of the cloth.
So cost is 100,
profit is 40,
Price is 140,
so 40/140 is profit.

Furtive Bertie.
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LVL 10

Expert Comment

ID: 10843578
Well, our points of vue differ :)
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LVL 33

Expert Comment

ID: 10845521
This is still the Puzzles and Riddles section, not the Math and Science section, so there must be a trick answer.

Pick at the wording of the question, and it says "What is his length of the metre scale?"  Not length of the improper metre scale.  So the answer is 1 metre (or meter, for those of us this side of the pond).

Also this side of the pond, we call them meter sticks or meter rulers, and reserve "scales" to mean a device used to measure the weight/mass of an object, the platelike skin of reptiles and fish, or running your fingers up and down the piano.  Cloth is sold by length, not weight, so the first one is out.  Cloth is not usually made from animal skin (unless it's leather), so the second one is out.  Therefore, this must be the third answer.  A piano is about 150cm wide, and has 88 keys, with 12 piano keys in an octave.  So the answer is roughly 4.9 octaves/meter.
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Expert Comment

ID: 10848080
snoyes_jw -

I think you might have something there - it does say "What is the length of the metre scale?"
Not the improper metre scale.

ie 1 metre.

:-(

Furtive Bertie.

Mercantilum -

I can see your point of view - but the question says "he make 40% profit", not "40% of what he charges is profit".  I suppose you could read both of those either way, but I think they each have a different meaning.

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LVL 5

Expert Comment

ID: 10848711
You only need to solve the following simple pair of equations:
S - C = 0.40*C
S/x - C = 0.39*C
where:
S is the sales price of 1m = what the merchant gets
M is the cost of 1m = what the mearchant pays
x is the length of the bad metre scale

The result:
x = 1.40/1.39 = 1.007

The bad measuring rod is about 7 mm too long.  The merchant gives away 7 millimetres for each metre he sells.  That's why he makes less profit.
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LVL 10

Expert Comment

ID: 10874894
Gross profit, or net profit?
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LVL 10

Expert Comment

ID: 10875007
Okay, okay... but seriously - directed to Mercantilum, and Furtive_Bertie:

In sales, a profit is simply the difference in dollars between the income and expense, or for a individual item, sale price and cost.  If you have an item that you buy for 60\$, and you sell it for 100\$, this is a 40\$ profit.  Divide the profit by the sale price of the item, and you get 40% - the profit margin for this transaction.  The thing to note is that the "markup" on this item is also 40\$, but the markup as a percentage is 66.66% (it is profit divided by the cost of the item).

If the cost of an item is 100\$, the profit is 40\$, and the price is 140\$, there is a 40% markup, but the profit margin is only 28.6%.

Since the question states profit as a percentage, I would assume they are refering to the profit margin.
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Expert Comment

ID: 10876116
eternal_21 & Mercantilium

It seems you are right.  That was not my understanding, but then again I program computers, not sell cloth :-)

For an indepth discussion I found the following post.  It seems I am not the only person to confuse profit & markup.
And as for Gross profit or Net profit - that seems even more confusing.  I found one definition which said gross profit was based on the cost of the item, whereas net profit wasbased on the cost plus all the intangibles such as wages, heating bills, rent, etc.

I'm glad I don't deal with this all day.  I can do the maths though.

Furtive_Bertie
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Expert Comment

ID: 10877913
So to use my previous calculation with a better understanding of what profit means :-))

SCALE 1
length = 1M
cost = c
Profit = .4
Price P = c/(1-profit) = c/.6

SCALE 2
length = L
cost = L * c
Profit = .39
Price = P  - SAME PRICE AS SCALE 1

PROFIT = (PRICE - cost)/PRICE

gives PRICE  = cost / (1-profit)

so we get the equations:

0.39 = ((c/.6) - Lc)/(c/.6)

cancel c

0.39 = ((1/.6) - L) / (1/.6)

0.39 * 1/.6 = 1/.6 - L

L = 1/.6 - .39/.6

L = (1-.39) /.6

L= (.61/.6)

gives L = 1.016666666.....

Furtive_Bertie
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Expert Comment

ID: 10878036
or 5/3 cm too long :-)
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LVL 10

Expert Comment

ID: 10882131
Furtive_Bertie, I calculated the same value.
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Author Comment

ID: 10886126
But,why should profit be .4 in the first case.It is 1+.4 and not .4 alone?
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Expert Comment

ID: 10886257

Profit is 40% - as you stated.

So profit is 40/100 times SOMETHING =>  0.4 times SOMETHING.

Furtive_Bertie

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LVL 10

Expert Comment

ID: 10886380
Hu... since the thread start to get lengthy,  padmapriya24 don't forget the 1st answer, ie mine, which is, I think true :)
You sell seomthing e.g. some cloth.
The cost of the cloth before you sell it, i.e. to buy the material, manpower etc... is, let say, C.
Now you sell it at a price P.
What is your profit ? Profit is  P-C.

So if you sell the cloth 1\$ and it gives you 40% profit, what is the initial cost C?
It is 100%-40% = 60%.
60% of what ? 60% of the 1\$....
E.g. 0.40 + 0.60 = 1.00

So - as an image - for 1 meter of cloth you sell, 0.40m is the initial cost, and 0.60m is your profit.

This is true when using a correct scale meter.
It happens that the seller does only 39% profit.

That means, that to come back to our previous image, that instead of getting  0.40m+0.60m=1m, with a correct 1m scale
he gets something like  0.39m + 0.60m = 0.99m
Or that he lost a bit of cloth x, which would have made the same meter scale as before:  (same image)

0.39m + 0.60m + x = 1.00m

x = 1 / 0.99 = 1.01
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Author Comment

ID: 10886562
but Mercantilum,
The trader makes a profit,(39%)in this case, due to the lesser length of the metre scale.Is this right?
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Expert Comment

ID: 10887097
to mercantilium.

You seem to be interchanging monetary values and percentages.

monetary value of profit = Price - cost.

Percentage  value of profit = ((price - cost)/price) * 100

we are given the percentages, not prices, so must use the second formula.

Furtive_Bertie
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LVL 10

Expert Comment

ID: 10890136
Yes padmapriya24, he makes a profit of 39%. In both cases he makes a profit.

If he would have a correct scale meter, he know he makes 40% profit.
But he actually makes only 39%. The reason is that the scaler meter is wrong.
If he makes less profit, it is because he gives more cloth to the client.
If he gives more cloth, it is because his scale meter his longer than 1 m:
- he thinks he's giving 1m, while he is giving more, therefore his profit is less.

So your question is the same as "How much cloth does he give more to the client which makes the profit being only 39%" ?
(refer to my previous answers for the result)
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Author Comment

ID: 10896331
mercantilium,
In the event of making a profit of 39%, i do accept that the metre scale is wrong.how do u say that the metre scale is longer than 1 metre.Why couldn't it be lesser than 1m?My assumption is , since the profit is 39%, the cloth sold is less due to the reduction in the metre scale.Do u accept this view point?
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LVL 10

Expert Comment

ID: 10896533
I understand your point of vue.
You say "look, I usually make a profit of 40%, but now it is only 39%, so, probably I sell less cloth, it is why I get less money".

If I sell you 1 m of cloth for 1\$, you would find logical, to say
"ok, for 1m of cloth, I give you 1\$ ; so if you give me 0.99 m of cloth, I pay only 0.99\$".

The thing is that our problem is not the same situation.

Let's take another example for you to see the point with exagerated figures:
- you buy gold, that you resell at a higher price
- let say you sell 1 kilo of gold for 1000\$, while you bought it 800\$

The profit is the difference between what you sell and what you bought.
What you sell is P for price, what you bought is B for buy.
So, your profit is   P - B.
profit is 1000\$ - 800\$ = 200\$

You understand that the lower B is, the higher your profit is.
e.g.  you can buy gold at B/2, your profit becomes P - B/2
e.g.  1000\$ - 800\$/2 = 600\$
You understand that the higher P is, the higher your profit is.
e.g.  you sell the gold 30% more expensive
e.g.  1.30*1000\$ - 800\$ = 500\$
At the opposite, the higher B is or the lower P is, the lower profit you make
e.g.  you buy gold for 900\$
e.g.  your profit is only  1000\$ - 900\$ = 100\$

Now, instead of reasoning with money, let's have the same reasoning with gold:

If you give less gold to the client for the same price, your profit will be higher...
e.g. 1 kilo of gold you sell is still 1000\$, but you give only 0.9 kilo that you bought 0.9*800\$ = 720\$   ;-)
e.g. your profit is higher in this case, since 1000\$ - 720\$ = 280\$   (> 200\$)

And finally - the opposite - if you give  more  gold to the client for the same price, your profit is lower
e.g. 1 kilo of gold you sell is still 1000\$, but you give 1.2 kilo instead of 1 kilo to the client! that you bought 1.2*800\$ = 960\$
e.g. your profit is lower, 1000\$ - 960\$ = 40\$ only.

In this last example, you see that it because you gave more gold to the client that your profit is lower.
This is the same for the cloth: the seller gave more cloth to the client.
How could he give more cloth? Simply because his scale meter is longer.

Graphically

<---scale meter giving length of cloth for 1\$---->

<---wrong scale meter giving longer length of cloth for still 1\$---->
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LVL 10

Accepted Solution

Mercantilum earned 160 total points
ID: 10896662
So to carry on with my explanation:
Profit = Price - Cost  <=>  40 = 100 - 60
If the seller gives more cloth for the same price, he misses some money which is the bonus cloth proportionnaly to the price he bought it
He bought the cloth 60 per meter, so x being the proportion of cloth he gives too much, we get
39 = 100 - 60x
That means that his profit becomes only 39 after he gave x time too much cloth that he bought previously for 60.
x = 61 / 60 ~=  1.017
That means he gaves 1.017 * the length of cloth he sells usually (1 meter) so the answer is the wrong scale is 1.017
This is what I always said, no??
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Author Comment

ID: 10896779
ok.I accept this answer of mercantilium.Thanks a lot to everyone who had helped me in arriving at this answer.
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Expert Comment

ID: 10897118

Mercantilum said:
"That means that his profit becomes only 39 after he gave x time too much cloth that he bought previously for 60.
x = 61 / 60 ~=  1.017
That means he gaves 1.017 * the length of cloth he sells usually (1 meter) so the answer is the wrong scale is 1.017
This is what I always said, no??"

Erm, NO actually, you said

"1 / 0.99 = 1.01 exact metre"

AND

"0.39m + 0.60m + x = 1.00m

x = 1 / 0.99 = 1.01"

:-(

Furtive_Bertie
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LVL 10

Expert Comment

ID: 10898565
That's right I gave initially a quick and dirty solution, taking as for initial cost both the bought cloth and the sold cloth.
But the idea behing the calculation was exactly the same.

According to padmapriya24's last posts, I think  his problem was more to understand what was behind the calculation i.e. the reasoning, that the exact figures,
even if they are important. It proves that it was more a personnal challenge for him to understand what we guys are doing, rather than completing a homework problem...

This is the last answer I gave without referring to the cloth problem (and therefore without the 61/60) which was accepted. This one did not explicit the cloth problem, only the reasoning based on the image of "selling some gold".
I corrected after my initial calculation (if I wouldn't have nobody would have noticed :) just to help padmapriya24's in case he tries on his own to find the same figure.

If you think you were the first to give the actual final figure (while noone accepted it and we still don't know if it is the right one :) and that you deserve some points, I guess the question can be reopened and padmapriya24's could share the points between you and me. padmapriya24's is the one to decide on this.

Regards
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