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# Alligation problem

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Alligation problem [#permalink]  05 Feb 2011, 10:11
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Question Stats:

0% (00:00) correct 100% (00:26) wrong based on 8 sessions
A dishonest grocer professes to sell pure butter at cpst price, but he mixes it with adulterated fat and thereby gains 25%. Find the percentage of adulterated fat in the mixture assuming that adulterated fat is freely available?

a)20%
b)25%
c)33.33%
d)40%
e)35%

Ans a

I am doing this by alligation using gain%

On selling at CP gain %=0
Required gain =25
Hence using graphical approach

0 100
\ /
25
/ \
x y

hence ratio of pure butter and adulterated fat x:y=75:25

or 3:1

% of adulterated fat in mixture 1/4*100=25%

Please tell me where I am doing wrong?
[Reveal] Spoiler: OA
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Re: Alligation problem [#permalink]  05 Feb 2011, 10:27
I got 20% as well.

Say 100g pure butter costs $100 But;$100 is his 25% profit because he just used 80gram pure butter.

80g would have costed him $80 and he sold it for$100 by adding 20g of freely available fat. $100 is 1.25(80) so; total weight=100g fat=20g 20% _________________ Manager Joined: 18 Oct 2010 Posts: 93 Followers: 2 Kudos [?]: 8 [0], given: 0 Re: Alligation problem [#permalink] 05 Feb 2011, 11:25 here is what i did a is the butter and b is the fat a / (a+b)=100%/125 125a=100 a +100b so 25 a=100b or a=4b b/(a+4b)=b/5b=1/5 or 20%? Intern Joined: 22 Jan 2011 Posts: 8 Followers: 0 Kudos [?]: 11 [0], given: 0 Re: Alligation problem [#permalink] 05 Feb 2011, 11:26 Actually can you tell me where I am doing wrong by using gain% in my method? Intern Joined: 22 Jan 2011 Posts: 8 Followers: 0 Kudos [?]: 11 [0], given: 0 Re: Alligation problem [#permalink] 06 Feb 2011, 02:15 Hi I was looking for a mistake in my approach...Somebody please help...In the method whr is the flaw?I am not able to figuare out Math Forum Moderator Joined: 20 Dec 2010 Posts: 2028 Followers: 138 Kudos [?]: 1158 [0], given: 376 Re: Alligation problem [#permalink] 06 Feb 2011, 07:18 sonuindia88 wrote: A dishonest grocer professes to sell pure butter at cpst price, but he mixes it with adulterated fat and thereby gains 25%. Find the percentage of adulterated fat in the mixture assuming that adulterated fat is freely available? a)20% b)25% c)33.33% d)40% e)35% Ans a I am doing this by alligation using gain% On selling at CP gain %=0 On selling adulterated fat gain%=100 Required gain =25 Hence using graphical approach 0 100 \ / 25 / \ x y hence ratio of pure butter and adulterated fat x:y=75:25 or 3:1 % of adulterated fat in mixture 1/4*100=25% Please tell me where I am doing wrong? I am not too good with alligation; But, you put the mean price of the mixture = 25%, which is not correct. It should be 4/5 So the diagram should look like; 0 100 \ / 80 / \ 20 80 Top Right = C.P. of 100 units of pure butter; say$100
Top Left = C.P. of 100 units of freely available fat; $0 So; S.P. for 100 units of mixture(butter+adulterated fat)=$100

Mean price = C.P. of 100 units of mixture = (100/(100+Gain%))*S.P. = (100/(100+25))*100 = $80 Bottom Right = Units of butter in 100 units of mixture = (80-0)=80; Bottom Left = Units of of freely available fat in 100 units of mixture = (100-80)=20 $$\therefore$$ Ratio of "free fat:butter"= 20:80 = 1/4 % of free fat in the mixture = (1/(1+4))*100=20% Ans: "A" _________________ SVP Joined: 16 Nov 2010 Posts: 1680 Location: United States (IN) Concentration: Strategy, Technology Followers: 31 Kudos [?]: 350 [0], given: 36 Re: Alligation problem [#permalink] 06 Feb 2011, 08:54 What does this mean : But;$100 is his 25% profit because he just used 80gram pure butter.
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Math Forum Moderator
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Re: Alligation problem [#permalink]  06 Feb 2011, 09:17
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subhashghosh wrote:
What does this mean :

But; $100 is his 25% profit because he just used 80gram pure butter. Rephrasing; The grocer is selling 100g of mixture(butter+fat) for$100. This $100 includes a 25% profit because he would have only spent$80 for 80g of butter and 0$for 20g fat. ***************************************** Actually a better example would be; Think that the grocer spent$100 for buying 100g pure butter. Now; in order to gain a profit of 25%, he will have to sell the same butter for $125. How he would do that? He would add 25g of fat(worth$0) to 100g of pure butter(worth $100) and sell 125g of mixture(butter+fat), saying that it is pure butter, for$125

Now you see;
125g of mixture is sold for $125 for which he had spent only$100. He made a profit of 25%.

125g of mixture contains 25g of fat; which is 25/125*100=20%
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Re: Alligation problem [#permalink]  06 Feb 2011, 09:37
100 * (b + f) - 100 * b = (25/100) * 100 * b
b = 4 * f
Percentage of f = (f / (b + f)) * 100 = (f/5f) * 100 = 20%
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Re: Alligation problem [#permalink]  07 Feb 2011, 20:34
1
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Expert's post
sonuindia88 wrote:
A dishonest grocer professes to sell pure butter at cpst price, but he mixes it with adulterated fat and thereby gains 25%. Find the percentage of adulterated fat in the mixture assuming that adulterated fat is freely available?

a)20%
b)25%
c)33.33%
d)40%
e)35%

Ans a

I am doing this by alligation using gain%

On selling at CP gain %=0
Required gain =25
Hence using graphical approach

0 100
\ /
25
/ \
x y

hence ratio of pure butter and adulterated fat x:y=75:25

or 3:1

% of adulterated fat in mixture 1/4*100=25%

Please tell me where I am doing wrong?

Alligation is used to find the average value given two values and the ratio of their weights. First of all, if average profit is 25%, what is the profit on the two individual items?
Profit on pure butter sold at cost price = 0%
What about profit on adulterated fat which is available free of cost? How is it 100%? Since its cost price is 0 and profit % = profit/CP * 100, profit% is actually infinite.
Secondly, the ratio that you get when you use alligation will be the ratio of their cost price, not the amount in which they are added. You need to be very careful about the weights you use.
When you are averaging Profit%, the weight will be Cost price because Profit% = Profit/Cost Price. Since denominator has total weight, weights will be cost price. Hence, do not use alligation in this question.

It can be very easily done using the method suggested above. Since profit is 25%, $4 of cost price gives$1 of profit. If cost of pure butter is $1 per gm, he used only 4 gm butter but sold 5 gm mixture. So 1 out of every 5 was adulterated fat i.e. 20%. _________________ Karishma Veritas Prep | GMAT Instructor My Blog Get started with Veritas Prep GMAT On Demand for$199

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Re: Alligation problem   [#permalink] 07 Feb 2011, 20:34
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