Find all School-related info fast with the new School-Specific MBA Forum

It is currently 20 Oct 2014, 13:34

Close

GMAT Club Daily Prep

Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized
for You

we will pick new questions that match your level based on your Timer History

Track
Your Progress

every week, we’ll send you an estimated GMAT score based on your performance

Practice
Pays

we will pick new questions that match your level based on your Timer History

Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.

Events & Promotions

Events & Promotions in June
Open Detailed Calendar

Alligation problem

  Question banks Downloads My Bookmarks Reviews Important topics  
Author Message
TAGS:
Intern
Intern
avatar
Joined: 22 Jan 2011
Posts: 8
Followers: 0

Kudos [?]: 4 [0], given: 0

Alligation problem [#permalink] New post 05 Feb 2011, 10:11
00:00
A
B
C
D
E

Difficulty:

  5% (low)

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
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?
[Reveal] Spoiler: OA
Math Forum Moderator
avatar
Joined: 20 Dec 2010
Posts: 2045
Followers: 128

Kudos [?]: 952 [0], given: 376

Re: Alligation problem [#permalink] New post 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%
_________________

~fluke

Get the best GMAT Prep Resources with GMAT Club Premium Membership

Manager
Manager
avatar
Joined: 18 Oct 2010
Posts: 95
Followers: 2

Kudos [?]: 7 [0], given: 0

Re: Alligation problem [#permalink] New post 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
Intern
avatar
Joined: 22 Jan 2011
Posts: 8
Followers: 0

Kudos [?]: 4 [0], given: 0

Re: Alligation problem [#permalink] New post 05 Feb 2011, 11:26
Actually can you tell me where I am doing wrong by using gain% in my method?
Intern
Intern
avatar
Joined: 22 Jan 2011
Posts: 8
Followers: 0

Kudos [?]: 4 [0], given: 0

Re: Alligation problem [#permalink] New post 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
avatar
Joined: 20 Dec 2010
Posts: 2045
Followers: 128

Kudos [?]: 952 [0], given: 376

Re: Alligation problem [#permalink] New post 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"
_________________

~fluke

Get the best GMAT Prep Resources with GMAT Club Premium Membership

SVP
SVP
avatar
Joined: 16 Nov 2010
Posts: 1691
Location: United States (IN)
Concentration: Strategy, Technology
Followers: 30

Kudos [?]: 297 [0], given: 36

Premium Member Reviews Badge
Re: Alligation problem [#permalink] New post 06 Feb 2011, 08:54
What does this mean :

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

Formula of Life -> Achievement/Potential = k * Happiness (where k is a constant)

Get the best GMAT Prep Resources with GMAT Club Premium Membership

1 KUDOS received
Math Forum Moderator
avatar
Joined: 20 Dec 2010
Posts: 2045
Followers: 128

Kudos [?]: 952 [1] , given: 376

Re: Alligation problem [#permalink] New post 06 Feb 2011, 09:17
1
This post received
KUDOS
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%
_________________

~fluke

Get the best GMAT Prep Resources with GMAT Club Premium Membership

Manager
Manager
avatar
Joined: 27 Oct 2010
Posts: 190
Followers: 1

Kudos [?]: 7 [0], given: 20

Re: Alligation problem [#permalink] New post 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%
Expert Post
1 KUDOS received
Veritas Prep GMAT Instructor
User avatar
Joined: 16 Oct 2010
Posts: 4870
Location: Pune, India
Followers: 1148

Kudos [?]: 5338 [1] , given: 165

Re: Alligation problem [#permalink] New post 07 Feb 2011, 20:34
1
This post received
KUDOS
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
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?


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

Save $100 on Veritas Prep GMAT Courses And Admissions Consulting
Enroll now. Pay later. Take advantage of Veritas Prep's flexible payment plan options.

Veritas Prep Reviews

Re: Alligation problem   [#permalink] 07 Feb 2011, 20:34
    Similar topics Author Replies Last post
Similar
Topics:
QUESTION OF ALLIGATION .. KaranSingh 1 24 Sep 2011, 11:43
mixtures and alligation -- please answer at the earliest dkj1984 4 31 Jul 2011, 01:29
Are Alligation and Mixture problems part of GMAT Quant ? vivgmat 2 11 Jul 2011, 08:00
1 mix and alligation xcusemeplz2009 2 16 Dec 2009, 02:18
1 Alligators from sets mbawaters 3 22 May 2008, 12:38
Display posts from previous: Sort by

Alligation problem

  Question banks Downloads My Bookmarks Reviews Important topics  


GMAT Club MBA Forum Home| About| Privacy Policy| Terms and Conditions| GMAT Club Rules| Contact| Sitemap

Powered by phpBB © phpBB Group and phpBB SEO

Kindly note that the GMAT® test is a registered trademark of the Graduate Management Admission Council®, and this site has neither been reviewed nor endorsed by GMAC®.