New Batches at TathaGat Delhi & Noida!
Average and Alligation
by Total Gadha - Saturday, 26 September 2009, 07:45 AM
 

cat average and alligation mixturesI recently read a student blog on TG Town questioning whether it is correct by the instructors to tell students “not to take their mock scores seriously.” After all, if a student is not performing well in mocks, something must be wrong. The question really made me ask myself the reasons for my saying so. Is it even correct to say mock scores do not matter. I think there are several reasons instructors tell students not to take their mock scores seriously. Most important of them all is motivation. Students are never ready to recognize that scoring well in a test is more a matter of temperament and question selection than that of content. In fact an average student having the art of question-picking would perform twice better than a genius student who is out to solve questions in a near about serial order. Therefore, instructors want to keep their students motivated in order to keep their enthusiasm high. The second reason for not taking mocks seriously is that the level of preparedness of students at a particular point is different. Many of the institutes start their mocks by the month of May or June and most students are not ready by then. It is inevitable that they will perform badly. If the students take it seriously, they would spend rest of their time taking more and more tests to improve themselves instead of studying and then the real harm would be done. For me, when I entered the CAT preparation, my verbal didn’t need preparation, my quant took three or four months of tweaking, but my DI took more than a year to reach a decent level. The level of preparedness for every student is different. So the question is, what do you do with your mock scores? The better thing to do is to solve your mock paper, if you can solve it on your own, you don’t have a problem with content. If you cannot, get back to studies. So don’t look hard at your scores, look hard at the paper.

The concept of averages is hardly a new concept at all. If asked, all of you would give me the following formula for calculating average: average formula. So far so good. But if I ask all of you to solve a simple problem many of you would reach for their pens.

The average score of three students A, B, and C is 50. When the score of another student D is added to the group, the average score become 47. What is the score of student D?

Answer: for most of you, the score of student D would be 4 × 47 -× 50 = 38.

For me, the calculation would just be 47 - 9 = 38.

Some of you might have understood what I did. Let me start explaining through a simple example. Then we shall extend our explorations to more complex problems.

averages

The two images above show two beam balances, one with equal arms and the other with the arms lengths in the ratio 1: 3. The dotted line in both cases shows the average value.

In the first beam balance, if you move any of the pan one unit towards the average value, the other pan would also move one unit in the direction of the average value to keep the average constant. For example, let the weights in the two pans be 50 kg and 60 kg. The average is 55 kg. If you increase the weight in 50 kg pan by one unit (i.e. 51) bringing it nearer to the average, you will have to decrease the weight in the other pan by one unit (i.e. 59), bringing it one unit nearer to the average, to keep the average constant.

In the second beam balance, if the arm of length 3 moves 1 unit towards the average, the arm of length 1 will have to move 3 units towards the average to keep the average constant. For example, let the weight in pan of 3 unit arm length be 40 kg and the weight in the pan of 1 unit arm length be 60 kg. Now if I increase the weight in the first pan by 1 unit, I shall have to decrease the weight in the second pan by 3 units to keep the average constant.

The same rule applies if I am moving a pan away from the average.

Now, understand this- the second beam balance can also be represented with a beam balance of equal arms but one arm having thrice the weight on the other arm. Savvy? Now let’s see the problem once again.

The average score of three students A, B, and C is 50. When the score of another student D is added to the group, the average score become 47. What is the score of student D?

Answer: Now there are three weights on one arm. The average of the four weights is 47. To move each of the three weight 3 units away from the average (50 - 47) I shall have to move the weight D 3 × 3 nine units away from the average. Therefore, weight D = 47 - 9 = 38.

Four friends have an average weight of 68. If Rahim is also included in the group, the average weight becomes 72. what is Rahim’s weight?

Answer: Same process: there are four people at a distance of 4 units from the average weight of 72. To balance them, we will have to place a person at 4 × 4 = 16 units from 72 on the other side. Therefore, Rahim’s weight = 72 + 16 = 88.

A batsman in his 20th innings makes a score of 93 and thereby increases his average by 3. What is the average after 20 innings?

Answer: If you have understood what I have said so far, the new average is nothing but 93 - 57 = 36. Let the new average be A. Therefore, there are 19 scores at a distance of 3 units from A. To balance these scores we need one score (which is 93) 19 × 3 = 57 units from A on the other side. Therefore A = 93 - 57 = 36.

Now let’s see this funda of ‘balancing act’ applied in a small part of a DI set from CAT 2006. For more DI sets based on averages, you will have to visit our CAT CBT Club

cat 2006 average DI

What is Dipan’s score in paper II in English group?

Answer: Rather than any long and cumbersome method, we can do this question in a very short and sweet way- we just see the deviation of each group average from the overall average. Now the average of PCB group is 98 which is +2 from overall average. Mathematics group is -1, Social science group is -0.5, Vernacular group is -1. Therefore, total so far = 2 -1 -0.5 -1 = -0.5. Therefore to have deviation from overall average as 0, the English group average should have a deviation of +0.5, i.e. the average should be 96.5. Therefore, Dipan’s mark in paper II in English group are 97.

Let’s have a look at the unbalanced scale in the figure 2 again. The beam balance is shown below:

averages

If you want to keep the average same while changing weights in both the pans, the weights in the pan would be inversely proportional to arm lengths, i.e. to increase the weight in the left pan by one unit, we shall have to increase the weight in the right pan by three units to keep the average constant. Here, the arm lengths signify the distance of the weights from the average. Let’s take a simple example:

For example, let’s mix two solutions one with 30% milk and the other with 75% milk. Let it be given that the mixture is of 50% milk. Now the distances (arm lengths) of both percentages from the average percentage are 50 – 30 = 20% and 75 – 50 = 25%. Since the arms lengths are in the ratio 20: 25 = 4: 5, the weights in the pan should be in the ratio 5: 4. Therefore, we are mixing the solutions in the ratio 5: 4.

alligation funda

Let’s see some examples now:

In what ratio must the rice at Rs 3.8 per kg be mixed with rice at Rs 4.5 per kg so that the price of the mixture is Rs 4.2 per kg?

Answer: By now, I believe you know what to do. The distances from the averages are 4.2 – 3.8 = 0.4 and 4.5 – 4.2 = 0.3. the distances are in the ratio 4: 3, therefore, the rice should be mixed in the ratio 3: 4.

A butler stole one-fourth of a wine bottle containing 60% alcohol and replaced it with water. Find the resultant concentration of the wine in the bottle.

Answer: Again an easy one with a little twist- now we are mixing three-fourth solution containing 60% alcohol with one-fourth solution containing 0%. The ratio of the quantities taken is 3/4 : 1/4 = 3: 1. Therefore, the ratio of the distances from the average would be 1: 3. Therefore, we Therefore, average value = 60% - 60 x 1/4 = 45%.

 

In a wildlife sanctuary, the counting of Zebras and Ostriches is being done. It was found that there were 150 heads and 480 legs. How many Zebras were there in the sanctuary?

Answer: No mixture here? Yes but there is! Zebra being the milk and Ostriches being the water. How can you use Alligation here. Simple, you first need to determine of what value we can take the average. Also, if you see what is the basic difference between a Zebra and an Ostrich that has been considered in the problem here, you will realize it is the number of legs- Zebra has four and Ostrich ahs two. And what is the average number of legs per animal given? It is 480/150 = 3.2. The distances from the average are 3.2 – 2 = 1.2 and 4 – 3.2 = 0.8. These distances are in the ratio 3: 2 or the quantities are in the ratio 2: 3. Therefore, the number of Zebras = 150 × 3/5 = 90.

 

alligation question

What percentage of the females polled said Yes?

Answer: Alligation over here? Yes sir, because we know the average percentage of males and females, i.e. 50% (number of males and females are equal). Now let’s just consider the percentage of males in those who said yes and those who said no. The corresponding percentages are 60% and 20% respectively. Let the ratio of the number of people who said yes and the number of people who said no be x : y. The ratio of distances of the percentages from the average percentage is (60 – 50): (50 – 20) = 1: 3 Þ x: y = 3 : 1. So let there be 200 people in all (100 males and 100 females). The ratio of people saying yes to people saying no is 3: 1. Therefore, number of people saying yes = 200 × 3/4 = 150, out of which females are 40% = 150 × 40/100 = 60 females said yes which is 60% of 100 females.

 

 

I am afraid I shall have to end here and leave the rest of it for my CBT Club students. I shall cover some DI sets based on averages and Alligation in the CBT Club this week.

 

Bookmark and Share
Re: Average and Alligation
by A S - Saturday, 26 September 2009, 07:46 AM
  As usual, another piece of gem from TG...you are awesome!!!
Re: Average and Alligation
by azfar niyazi - Saturday, 26 September 2009, 07:47 AM
  thanks tg for ur support ,read it felt awesome

i have one problem ,i am very bad in quant how should i improve it in just1 months ,should i only look at the basics

looking for ur reply
Re: Average and Alligation
by Kirubakaran kaliaperumal - Saturday, 26 September 2009, 10:47 AM
 

Hi TG,

I agree with your point. But I am not sure if right question picking strategy is going to be of much help in a CBT. According to CAT demo found in the official CAT website, I think it is very difficult to pick the right questions. Please give some pointers about this...

Re: Average and Alligation
by Rajarshi Guha - Saturday, 26 September 2009, 10:58 AM
  TG Sir,

Amazing.!!!I cannot help but marvel at the lucidity of your brain and the pristine beauty of mathematics.

More such lessons are awaited with CAT being just around the corner Sir.


cheers
Re: Average and Alligation
by wannabe blacki - Saturday, 26 September 2009, 11:17 AM
 

wonderful sir!! thanx forbringin abt our emancipation from the equations and variables for solving problems like these,that are basically founded on one's commonsense. reading ur articles makes me realise,yet again,why THE indian mind is a respected entity all over the world...

thank u  sir!

Re: Average and Alligation
by Ronak kabani - Saturday, 26 September 2009, 12:38 PM
  Dear Sir
Awesome as usualsmile
Ronak
Re: Average and Alligation
by amit kheterpal - Saturday, 26 September 2009, 02:59 PM
 

1)A butler stole one-fourth of a wine bottle containing 60% alcohol and replaced it with water. Find the resultant concentration of the wine in the bottle

 

2)What percentage of the females polled said Yes? 
      

 

sir, ca u pls explain these two question more deeply ..iam not able to understand them..

Re: Average and Alligation
by ritesh gupta - Saturday, 26 September 2009, 09:34 PM
 

hi sir,

thanx 4 the article,

i was waiting 4 dis coz i m just completing my basics

nice day everybody........

Re: Average and Alligation
by Bonhomie Fella - Sunday, 27 September 2009, 02:03 AM
  SIR jiiiiiiiiiiii kahan they aap!!!!!! every now and then i use to log in to totalgadha.com with the hope of seeing another magnum opus from a magnum opus........... but this time you made us wait quite a lot Sirsad...... pls dont leave us.. i still remember back in 2007 the site was pouring with articles, we at least demand an article or some gyan from you fortnitely, plssssss sir, itna to banta hai !!!!!!! thanks for this one Sir, may God Bless You !
Re: Average and Alligation
by Jaidev Nair - Sunday, 27 September 2009, 02:51 AM
  Thanks TG,

Your way of seeing things in different ways is excellent.

thanx
by shivam mehra - Sunday, 27 September 2009, 11:12 AM
  keep going sirji..thanx a lot..
atlast there is something to cheer even after india's defeat to pak
Re: Average and Alligation
by Neeraj Rawat - Sunday, 27 September 2009, 08:00 PM
  Awesome post Sir..
Re: Average and Alligation
by jatin mehta - Monday, 28 September 2009, 09:01 AM
  I'd attempted the '06 DI ques in routine way. bt this way wz pure TG magic.blush
Marriage poll ques. is subtle.
Tnx TG .
Re: Average and Alligation
by arun kumar - Monday, 28 September 2009, 07:11 PM
  i guess that iS the differnce b\w mortals n the great TG..LOLS..
Re: Average and Alligation
by Amit Sharma - Tuesday, 29 September 2009, 10:28 AM
  good one
Re: Average and Alligation
by Total Gadha - Tuesday, 29 September 2009, 01:55 PM
  Hi Kirubakaran,

As the computer-based CAT is going to have a one-question-per-page format the question selection skill needs to be sharpened more than ever. The biggest challenge a student is going to face is whether he/she should attempt a particular question or move on to the next one.

I see you are in CBT Club already. We will talk about the strategy there only shortly.

Total Gadha
Re: Average and Alligation
by rohit dwivedi - Tuesday, 29 September 2009, 05:37 PM
  TG sir , why " there only ".
We are also deprived and old student of yours.
Need your benovalence..
Re: Average and Alligation
by rahul m - Tuesday, 29 September 2009, 06:32 PM
  hello....

didnt got last Q ...
how 1 :3 also ratio of yes :no person....????

shoulnt be 1:3 ratio of only MEN yes:No........howcome womens too included...?
Re: Average and Alligation
by rohan kir - Tuesday, 29 September 2009, 06:59 PM
 

Hi TG

am new to this forum . i am also interested in joining the cbt club but am a bit skeptical as to whether it will help me that much as only  a couple of months are left .also wanted to inquire as to how frequently the core topics will be discussed and whether detailed solutions of the questions which trouble us wil be provided or not.the thing is that i am also giving aimcat series but am not able to convert the 90 %ile scores into the big ones largely due to DI.

Re: Average and Alligation
by Vaibhav Srivastava - Tuesday, 29 September 2009, 09:20 PM
  Hi TG sir .

I am writing this post just to thank you for the fabulous job that you are doing . I am a technical consultant with IBM for the past 2 yrs and have decided to hit back to B schools . My hectic project schedules mean that I don't have the luxury for coaching classes .Your wonderful articles have given me the opportunity to compete at the best level .

Thank you again !!
Re: Average and Alligation
by Mansi Pakhi - Wednesday, 30 September 2009, 12:00 AM
 

Hi TG and Dagny

I did'nt know how to reach to you for this singular problem that i am facing, As this is currently the most active post..i writing down here only.

I feel that RC quizz is a waste without explaining or atleast providing correct answers for all...the attempt is limited only to 5 for like 25 passages.

After attempting 5-6 RC...i get eager to know the correct answers...you know how frustating it is when you choose the wrong answers...My mind gets fixed to it...and eventually it leaves me  with this intractable disposition.

Please help me..out and suggest sumething

Re: Average and Alligation
by Total Gadha - Wednesday, 30 September 2009, 12:09 AM
 

Hi Mansi,

When you submit the test you would see the options with white background , they are the correct answers.

 

Re: Average and Alligation
by punam lade - Wednesday, 30 September 2009, 07:53 AM
 

Hello TG

 

I didn't get the solution to the last problem.The average that you have considered is 50%.That is you keep both the men and women on the two sides of the pan .Men on one side women on other side.But the average that you are carrying out is only of men 60-50 and 50-20 (both 60 and 20 refer to men who speak yes or no)instead of men and women to get to get to the average at 50%.Can you exaplin this

 

vanila

Re: Average and Alligation
by jai singh - Friday, 2 October 2009, 12:24 PM
  Totally awesome sir....
Re: Average and Alligation
by Syed Ahsan - Saturday, 3 October 2009, 12:44 PM
  I liked the simple and elegant example for allegation(distance from avg. )
Re: Average and Alligation
by - SK - Wednesday, 7 October 2009, 07:26 PM
  Thank you so much sir..
Re: Average and Alligation
by sujay singh - Sunday, 11 October 2009, 01:06 PM
 

TG is being a bit selfish when he says that "Will share the qn selection strategy in classes" .... Cummon TG !!! You have done so much ... going all the way in helping people when it comes to guys apart from coaching fellows .... So why not write a sentence or two sharing such strategies also ... that wont take anything aways from you ... Rather Will contribute to you non ending Glory as the best online CAT helper...

Was just an advice. .... Never meant to Hurt you .... You Rock anyways !!

Re: Average and Alligation
by aparna daga - Monday, 12 October 2009, 10:08 AM
  fantastic post sir! thank you so much smile
Re: Average and Alligation
by vinay kumar P - Tuesday, 13 October 2009, 11:41 PM
  hi punam lade and rahul

The approach explained is something like this..

We know the percentage of boys ( say % of alcohol) in both those who tell the truth (say variety 1 ) and those who tell false (say variety -2)

The ratio in which we mix these to varieties , to yield a final mixture in which we have 50% boys is what was found out.

which is 50 - 20 : 60 - 50 or 3:1 (as per the explained principle)

Say we have 3 truth tellers and 1 liar

When mixed we get 4 , or 2 boys and 2 girls (equal nos of boys & girls)

Girls who tell truth = 3 * 0.4 (as 40% of truth tellers are girls)

therefore , % of total girls who tell truth = 3 * 0.4/ 2 = 0.6 or 60%


Re: Average and Alligation
by rupasree raj - Tuesday, 20 October 2009, 10:23 AM
  hi TG sir, 
  first of all, thank you for such a great article....
               sir, pls help me in dis problem in de way u've explained above.

Qs: The average score in mathematics of a class of 36 students is 60. if de top two scores are excluded, de average goes down by 2. if de second highest score of de class is 90, find de highest score of de class?
a) 95
b) 96
c) 97
d) 98
e) 100
Re: Average and Alligation
by vinay kumar P - Tuesday, 20 October 2009, 11:23 AM
  @rupashree

If the two students are removed say with 60 marks each, the avg would have remained the same at 60.But as per the question it has become 58.So an extra marks of 34*2 has also been taken along with 120.So add 34*2 to 120 which becomes 188.

Subtract 90 , which gives the topper's score as 98.
Re: Average and Alligation
by rupasree raj - Wednesday, 21 October 2009, 07:13 PM
  thank you very much.....smile
Re: Average and Alligation
by harish kothari - Thursday, 22 October 2009, 01:06 AM
 

TG sir ,

 

In cases of mixtures teh concept is well understood . but i still have doubts and lack of clarity when it is used in like group of people ,people leaving the group or replacement of an individual.

Re: Average and Alligation
by Total Gadha - Thursday, 22 October 2009, 12:11 PM
  Harish,

Example please?

Total Gadha
Re: Average and Alligation
by kaushik roy - Monday, 26 October 2009, 11:41 AM
 

Respected TG Sir,

1.There is a group of 10 people of average age 50. One member of the group of age 70 left and two new member of age 25 and 80 joined the group. Wht would be the final average age of the group.

2.Also TG sir, please discuss the last year cat DI question ( 4 dept HR ,marketing ,Finance etc..a table was given).

Regards, 

Kaushik

 

 

Re: Average and Alligation
by sahil batra - Monday, 26 October 2009, 12:33 PM
  Kaushik its
1) 48.63
Re: Average and Alligation
by Priyesh Tungare - Wednesday, 28 October 2009, 11:44 AM
  In a wildlife sanctuary, the counting of Zebras and Ostriches is being done. It was found that there were 150 heads and 480 legs. How many Zebras were there in the sanctuary?

In this question, Why did we multiplied 150 heads by 3/5? Please explain.


Re: Average and Alligation
by vinay kumar P - Wednesday, 28 October 2009, 04:43 PM
 
@ kaushik

Replacing a 70 kg man with two having 80 and 25 can be viewed as letting the 70 kg man remain and add a 35 (80+25-70) kg man to the first group.So that the avg becomes
50 - 15/11 ( 535/11 = 550/11-15/11)
= 48.63
Re: Average and Alligation
by sahil batra - Thursday, 29 October 2009, 10:41 AM
  this ques. can be solved simply by use of equation.i.e.
x+y=150
4x+2y=480
where x=zebras,y=ostriches.....

please explain the butlers question

butler stole one-fourth of a wine bottle containing 60% alcohol and replaced it with water. Find the resultant concentration of the wine in the bottle.

I'm not able to get it..sad
Re: Average and Alligation
by ROHIT K - Thursday, 29 October 2009, 11:32 PM
  Hi Sahil,

Just a different take on the butler question.

Let there be 100 litres of solution

Alcohol          Water
60                    40

Butler removed 1/4th of the alcohol from 100 litres i.e. 25 litres hence 75 litres remain.

This 75 litres will contain again 60 % alcohol

Alcohol  = 60%of 75 = 45 litres alcohol in 100 litres of mixture(75 litre mixture + 25 litre replaced water) since he replaced 1/4th of alcohol with water. So quantity of water will increase to make the mixture 100 litres without disturbing the quantity of alcohol in the mixture.

Hence the concentration of alcohol is 45%

Hope this helps. smile



Rohit
Re: Average and Alligation
by sahil batra - Monday, 2 November 2009, 08:57 PM
  Damn....that was too easy...I was making it difficult...
Thanx Rohitsmile
Re: Average and Alligation
by sumit agarwal - Tuesday, 3 November 2009, 05:12 PM
  Assume all are zebra ...

so 150 heads --->>>300 legs...

but actually 480 legs.. so 180 legs are coming from ostrich ..who has 4 but we counted only 2(assuming they were zebra)

ostrich 180/2 =90
Re: Average and Alligation
by Saurabh - confusion fused - Monday, 23 November 2009, 12:19 AM
  Hello TG Sir,

I solved the last problem my own way. I am not understanding the mistake I made.

Out of all those who said YES, 60% were male, so  40% were females. ----(1)
Out of all those who said NO,  20% were male,'coz 80% were females. ----(2)

Now,
Keeping statement (1) in mind let's say 60 males said YES and 40 females said YES.
Keeping statement (2) in mind let's say 20 males said NO  and 80 females said NO.

So,
total males   = 80  => Yes=60, No=20
total females =120 => Yes=40, No=80

So, percentage of females who polled YES = females who polled YES/total females
= 40/120 = 1/3 = 33%

Please clarify where I went wrong...or such type of thinking is altogether different? and more importantly...wrong?

Regards,
Saurabh
Re: Average and Alligation
by Saurabh - confusion fused - Monday, 23 November 2009, 12:30 AM
  Hello TG Sir,

I solved the last problem my own way. I am not understanding the mistake I made.

Out of all those who said YES, 60% were male, so  40% were females. ----(1)
Out of all those who said NO,  20% were male,'coz 80% were females. ----(2)

Now,
Keeping statement (1) in mind let's say 60 males said YES and 40 females said YES.
Keeping statement (2) in mind let's say 20 males said NO  and 80 females said NO.

So,
total males   = 80  => Yes=60, No=20
total females =120 => Yes=40, No=80

So, percentage of females who polled YES = females who polled YES/total females
= 40/120 = 1/3 = 33%

Please clarify where I went wrong...or such type of thinking is altogether different? and more importantly...wrong?

Regards,
Saurabh
Re: Average and Alligation
by mba 2009 - Monday, 23 November 2009, 04:22 PM
  @Saurabh
My dear friend in the question it is mentioned that no. of males is equal to no. of females, but in your approach they are different.

mayank
Re: Average and Alligation
by ankush rastogi - Wednesday, 3 February 2010, 03:51 PM
  hi,
answer will be 98
as
old average=36*60
and 36*60=34*x+y+Z
58*34=34*x
therefore x=58
z=90
therefore y=98
Re: Average and Alligation
by amu ameya - Wednesday, 7 April 2010, 07:29 PM
  @ saurabh
From ur solution wat u are inferring is that there were 200 people and 100 said yes and 100 said no which is a wrong assumption
Re: Average and Alligation
by Pravin Vaidya - Monday, 31 May 2010, 06:52 PM
 

What percentage of the females polled said yes??

--This can be solved using simple equation as well...

Let us consider x and y to be the no. of persons who said yes and no respectively.

Therfore, to tal no. of females can bewritten as,

0.4*X +  0.80*Y  = 100  --- (1)

as we already know, X+Y = 200
Thus, equation 1 can be wriiten as,

0.4*X + 0.80*( 200-X) = 100

X = 150

and Y = 50.

so, percenatge of females polled said Yes , can be written as,

= 0.4* X/ 100 = (0.4*150)/100
= 60 %  ....  smile

Re: Average and Alligation
by abhishek rai - Tuesday, 1 June 2010, 07:49 PM
  Hi Tg Sir.

Here is a problem, where I need help
Q. The average of 7 consecutive integers is 7. Find the average of the squares of these integers.

Also, in the following problem, Solution can be obtained by using equation, can we do it using any other simple method:

There were 35 students in a hostel. If the number of students increases by 7, the expenditure of mess increase by Rs. 42 per day while the average expenditure per head diminishes by Re. 1. Find the original expenses of the mess.

Regards
Abhishek
Re: Average and Alligation
by deepti anand - Tuesday, 1 June 2010, 11:45 PM
  hii abhishek

4 d 1st prob...accordin 2 me..d ans ll b 53...its given avg of 7 consecutive integers is 7...so v can take d 1st integer as "x",den d 2nd consecutive integer ll b "x+1",nxt ll b "x+2"...so on..till d last no..which ll b"x+6"...
total no is 7...avg is also 7...so ll gt "x" as 4...

so v gt 1st integer as 4,nxt ll b 5....nd d last 1 ll b 10...sqin d nos...v gt 371 as total...total no is 7..i.e d total obsevation..so d avg ll b 53...
Re: Average and Alligation
by deepti anand - Tuesday, 1 June 2010, 11:51 PM
  hii tg sir,

i hv a prob:
a shopkeeper mixes 3 varities ig wheat costin rs 12,rs14,nd rs 17 per kg. Find d ratio of mixin of varities if d mixture is sold at rs 15 per kg nd he gains 20% profit??

actually, i always find prob in ques where 3 varities r mixd....plz do help me..
Re: Average and Alligation
by abhishek rai - Wednesday, 2 June 2010, 12:03 AM
  Hi Deepti
Thanx for the answer. Will try for a method which is less cumbersome though.
For your question.

The answer should be 9:3:1.

See, if he is selling at a cost price of Rs. 12.5, then he would get 20% profit. So, his deviations from 12.5 are .5, 1.5 and 4.5, i.e 1;3:9. So he must mix them in the ratio 9:3:1.

Do let me know if I m correct.
Re: Average and Alligation
by deepti anand - Wednesday, 2 June 2010, 08:10 PM
  hii abhishek..
 thanx for the ans...ya ans is ryt...its 27:6:1...
Re: Average and Alligation
by deepti anand - Thursday, 3 June 2010, 08:56 PM
  hii abhishek...
typin  mistake..i meant its wrong...nyways thanx...
Re: Average and Alligation
by abhishek rai - Thursday, 3 June 2010, 11:06 PM
  Hi Deepti
Can you plz explain the answer?
Re: Average and Alligation
by In lonely planet i live - Tuesday, 8 June 2010, 09:31 PM
 
a shopkeeper mixes 3 varities ig wheat costin rs 12,rs14,nd rs 17 per kg. Find d ratio of mixin of varities if d mixture is sold at rs 15 per kg nd he gains 20% profit??

Can anybody explain the answer please.....
Re: Average and Alligation
by abhishek rai - Tuesday, 8 June 2010, 10:55 PM
  Since he is selling at 20% profit, he must be selling at Rs. 12.5.

So his cost price is Rs.12.5

Hence,

12a+14b+17c = 12.5 (a+b+c)
=> 1.5b+ 4.5c=.5a
=> 3b+ 9c= a

Now, check the answer. There's not going to be any unique answer. For example, for b=1 and c=1, we have a= 12. so one of the answers is 12:1:1. Similarly, we can have 24:2:2 or 27:6:1.

Hope you get it.
Re: Average and Alligation
by In lonely planet i live - Wednesday, 9 June 2010, 12:22 PM
  Thanks dude.Gr8 equation...!!!
Re: Average and Alligation
by In lonely planet i live - Sunday, 30 January 2011, 05:01 AM
  Gr8 article. Hats off!!!!!
Re: Average and Alligation
by vicky singh - Friday, 4 February 2011, 07:23 PM
  Hello TG sir
great article..hats off....
but sir tell me how to solve allegation ques. in which 3 quantites are given like same as ur question with changes?

In what ratio must the rice at Rs 3.8 per kg be and Rs. 5.8 mixed with rice at Rs 4.5 per kg so that the price of the mixture is Rs 4.2 per kg?

pls reply TG sir
Re: Average and Alligation
by In lonely planet i live - Friday, 25 February 2011, 10:31 PM
  Hi everybody,

I just want some clarification regarding the below question:

The cost of marble is directly proportional to the weight. Marble is broken and it got divided in the ratio of 3:4:5, if marble had broken into three equal parts by weight then there would have been a further loss of 1800. Whats the cost of original marble ( unbroken).

choice:
3600, 10800, 2160, none of these.
Re: Average and Alligation
by swagata mukherjee - Thursday, 12 May 2011, 08:16 PM
  to vicky singh,
this is a short-cut method
let 3.8 kg & 5.8 kg has to be mixed in the ratio x:y
x                    y
3.8                 5.8
                                     (subtract in cross)
           4.2

5.8-4.2         4.2-3.8
=1.6                =0.4 

now x:y=1.6 : 0.4 = 4:1
so,they must be mixed in the ratio 4:1
hope this is clear!!!
         
      
Re: Average and Alligation
by Siddarth Paul - Thursday, 26 May 2011, 06:15 PM
  There were 35 students in a hostel. If the number of students increases by 7, the expenditure of mess increase by Rs. 42 per day while the average expenditure per head diminishes by Re. 1. Find the original expenses of the mess.

Can you please explain the solution?
Re: Average and Alligation
by TG Team - Friday, 27 May 2011, 11:22 AM
 
Hi Siddharth smile

You could have done in many ways.

First-normal math way - Let x be the original daily per head expenditure. So equating daily expense calculated in two ways, we get: 35x + 42 = 42(x - 1)
=> x = 12.

Second - Just look for the difference in expense per head. Due to addition of 7 students, expense of Rs 42 has been added and expense per person is decreased by Re 1. So total expense for the 7 new students = 35 + 42 = 77 i.e. 11 per head.
=> Original expense per person is 11 + 1 = 12.

Kamal Lohia
Re: Average and Alligation
by RITABAN SENGUPTA - Monday, 20 June 2011, 09:57 AM
  Hi Sir,

I have a problem in understanding as to how you are adding,35+42 to deduce the result.

42 is the increase in expenditure,but what I didnt get was how come 35 is added to it.
thoughtful thoughtful

Could you also please solve the problem of marvel posted above by one of our friends?? I tried but could not do it.
Re: Average and Alligation
by TG Team - Monday, 20 June 2011, 12:40 PM
 
Hi RITABAN SENGUPTA smile

See that there are 35 students in all and their expediture per head is getting reduced by 1. That means the new 7 students has 35 more rupees (taken 1 from each of 35 students) other than the increased expenditure of 42 rupees for their own well-being. So in all these 7 students have 35 + 42 = 77 rupees which they can share 77/7 = 11 each.

I hope this is clear now. smile

Kamal Lohia

Re: Average and Alligation
by RITABAN SENGUPTA - Tuesday, 21 June 2011, 11:57 PM
  Hi Sir,

Thank You.Now i have a clear picture of the question.But sir I have one more request,could you please kindly solve the question on marvel posted above?? I tried twice but couldnt do so.

Thanks again.
Re: Average and Alligation
by neha lahoti - Thursday, 23 June 2011, 09:39 PM
 
The students of three classes A,B,C take a test.the average per student marks of the classes A and B put together is 71.Av marks per student of B and C put
together is 76.Then av per student marks of A and C is 79. Find range of the average marks(p) of all the three classes put together.
ans:73.5 <p <77.5

pls solve
Re: Average and Alligation
by destiny unruled - Friday, 24 June 2011, 03:03 PM
  (ax + by)/(x + y) = 71
=> ab + by = 71(x + y)

Similarly,
by + cz = 76(y + z)
and cz + ax = 79(x + z)

Adding all we will get
ax + by + cz = (75x + 73.5y + 77.5z)

=> Average of all = A = (ax + by + cz)/(x + y + z) = (75x + 73.5y + 77.5z)/(x + y + z)

Now, we can see that minimum will be greater than 73.5 and maximum will be less than 77.5.

Hence, 73.5 < A < 77.5
Re: Average and Alligation
by neha lahoti - Friday, 24 June 2011, 09:03 PM
  Thank u so much.. G for genius smile
Re: Average and Alligation
by gaurav midha - Saturday, 25 June 2011, 06:40 PM
  nice article..smile
Re: Average and Alligation
by naveet KUmar - Tuesday, 12 July 2011, 05:38 PM
 

The concentration of three milk solutions A,B and C are 10%,20%,30% respectively.They are mixed in the ratio 2:3:N resulting in a 23% concentration solution.Find N.

 

Can you please tell me how to solve this one???

Re: Average and Alligation
by Rakesh Patil - Friday, 5 August 2011, 05:12 PM
 

@Navneet:

sol->

-> (10*2 + 20*3 + 30 N)/(2 + 3 + N) = 23

-> solve this equation

-> N = 5

cool

 

Re: Average and Alligation
by suraj saxena - Tuesday, 1 November 2011, 07:30 PM
  HI TG
QUES. AN AVERAGE AGE OF EMPLOYEES IN ACOMPANY IS 35 IF 5 MORE PERSONS ARE ADDED WITH AN AVERAGE AGE OF 32 YEARS THE AVG. AGE OF COMPANY BECOMES 34.HOW MANY PEOPLE WERE THERE INITIALLY.

HOW TO SOLVE THROUGH THIS METHOD.
Re: Average and Alligation
by piyush gupta - Wednesday, 9 November 2011, 09:23 PM
  Hi suraj,
The Avg. age of 5 employees is 32
Avg. Age of initial emp. is 35
New Avg. is 34

Now the diff. in avg. is in the ratio of 2:1

So, the no. of ppl. will be in the ratio of 1:2

So, for 5 ppl. of 32 age, 10 ppl of 35 age are needed to get avg. of 34.

I hope this helps
Re: Average and Alligation
by 50 cent - Monday, 12 March 2012, 12:27 PM
  even simpler way is... If 100 liters contian 60 percnt i.e 60 l alcohol then in 75 percent i.e 75 l. Vil have how much..... Hence,60*75/100 is 45...
Re: Average and Alligation
by 50 cent - Monday, 12 March 2012, 12:27 PM
  even simpler way is... If 100 liters contian 60 percnt i.e 60 l alcohol then in 75 percent i.e 75 l. Vil have how much..... Hence,60*75/100 is 45...
Re: Average and Alligation
by Arti Mehta - Saturday, 17 March 2012, 03:43 PM
  Hello evrybody!! smile

i solved the last question using another approach..

YES NO
3:2 1:4
Males:Females Males:Females

Let the multiplication factor in 3:2 ratio(for yes) be =x
and dat for 1:4 ratio(for no) be=y

Now since number of yes ppl= number of no ppl,
=>3x+y=2x+4y
=>x=3y

wot we have to calculate is
2x/(2x+3y)
=>6y/10y *100%
=>60%

which is the right ans..
now theres a problem! i want to find da ans to the same questiion if the percentage of the men and women are 55%:45%
i.e. 11:9

wen i calculate using my approach, i get 63.63%

whereas if i try using TG approach, I get 70%

can anybody plz clarify....? wot is the ryt answer..?




Re: Average and Alligation
by 50 cent - Saturday, 17 March 2012, 09:19 PM
  Plz tell me how to solv this..
A cask is filled with a mixture of 2 liqs. A n B in the proportion A:B:: 5:3. When 16 gallons of the mixture is drawn off and the cask filled with the liq B the proportion becomes A:B :: 3:5. How many gallons does the cask hold?


Re: Average and Alligation
by Arti Mehta - Saturday, 17 March 2012, 10:37 PM
  @ Siddharth..
Is it 40 gallons?
Re: Average and Alligation
by arsh arora - Monday, 19 March 2012, 02:03 AM
 

yes.. it is 40 gallons,

eqn used--3/5=5x-10/3x-6+16,this gives x=5

so original=3x+5x=40 hence the answer

Re: Average and Alligation
by 50 cent - Wednesday, 21 March 2012, 08:53 AM
  yus it is 40 .. Thnx Mr. N Ms. A...
Re: Average and Alligation
by tarun sahu - Thursday, 10 May 2012, 08:53 AM
  how do i know when to take lcm in ratio proportion questions.. 
Re: Average and Alligation
by TG Team - Thursday, 10 May 2012, 01:52 PM
 

Hi Tarun smile

Post some questions where you have doubt. Then it'll be easier to explain.

Kamal Lohia

Re: Average and Alligation
by vinny s - Monday, 16 July 2012, 10:01 PM
  hi sir ,
i have a doubt in a question

ques: A milkman has 6 cans , each of 10 litres of milk, of concentrations 20% , 30% , 40%, 50%, 70%, 80%. If he mixes from exactly 3 of the cans to form one litre of milk of exactly 50% concentration , in how many ways could he have selected the the three cans??
a: 14
b: 15
c: 16
d: 17


i solved it to make 30 litres of which i need to put 15 litres from any three cans so i got
the triplets as (8 , 5 , 2), (8,4,3), (7,5,3) and multiply by 3! to get 18 but the answer is 15???????????????
Re: Average and Alligation
by neha aggarwal - Sunday, 22 July 2012, 05:52 PM
  Hi Sir smile,

What is the best approach to do such questions:
"In what ratio 3 mixtures having concentration 40%, 60% and 90% be mixed so that resultant would be 67% solution."

I did it with distance between given mixture concentration an the concentration to be achieved and got: 7:27:12 as ans

Thanks,
Neha
Re: Average and Alligation
by vinny s - Sunday, 22 July 2012, 11:46 PM
  i did not get it ,, can u plzzz explain step by step??
Re: Average and Alligation
by TG Team - Tuesday, 24 July 2012, 07:27 AM
 

Hi Neha smile

There cannot be a unique solution to this one if there are not any other conditions attached.

See if I take 100x, 100y and 100z of the three solutions and mix them, then total quantity of mixture becomes 100(x + y + z) quantity and equating the quantity of sloute in the mixture, we get:

40x + 60y + 90z = 67x + 67y + 67z

=> 23z = 17x + 7y

Now this equation has many solutions, that's why I said no unique solution is possible unless some other restrictions are put.

Re: Average and Alligation
by neha aggarwal - Tuesday, 24 July 2012, 02:01 PM
  Hi Sir smile,

Thanks for your reply..
But i think, i did not understand the concept properly.. Can you shed some light on it.. Will be great help.

Neha
Re: Average and Alligation
by Anuj Asthana - Saturday, 25 August 2012, 07:19 PM
  Some important Questions for CAT please
Re: Average and Alligation
by Sonia Bajaj - Tuesday, 23 July 2013, 06:04 PM
  Hello Sir,

Read this question somewhere and I am pretty clueless.

a man had to distribute pencils to the kids of his town. When he was distributing, out of the 612 kids of his town, half of the girls and 3/4th of the boys were present. he gave 8 pencils to each girl and 12 pencils to each boy. how many pencils did he distribute in all?


Kindly help.

Thanks smile
Re: Average and Alligation
by Jim Moriarty - Monday, 10 March 2014, 12:14 PM
 
Hi TG,

This a question based on this write up. I've been breaking my head for days trying to comprehend it.

Your words:
"In the second beam balance, if the arm of length 3 moves 1 unit towards the average, the arm of length 1 will have to move 3 units towards the average to keep the average constant. For example, let the weight in pan of 3 unit arm length be 40 kg and the weight in the pan of 1 unit arm length be 60 kg. Now if I increase the weight in the first pan by 1 unit, I shall have to decrease the weight in the second pan by 3 units to keep the average constant. "

I'm representing your example statement
"the weight in pan of 3 unit arm length be 40 kg and the weight in the pan of 1 unit arm length be 60 kg"
as:
A1 = 40Kg, A2 = 60Kg with Aw = 55Kg.
                    3                           1
(A1)40-----------------(Aw=55)-----------------60(A2)
(60-55 = 5)                                            (55-40=15)
(n1 = 1)                                                      (n2 = 3)


Ratio in which the weights are mixed = 1:3 (After reducing ratio from 5:15)
Ratio of arm lengths = 3:1

Your next statement:

"Now if I increase the weight in the first pan by 1 unit, I shall have to decrease the weight in the second pan by 3 units to keep the average constant."

Based on your above statement, the figure is,

                   7                           1
(A1)41-----------------(Aw=55)-----------------57(A2)
(57-55 = 2)                                            (55-41=14)
(n1 = 1)                                                      (n2 = 7)


Ratio in which the weights are mixed = 1:7
Ratio of arm lengths = 7:1

Solving this: Aw = [(1X41)+(7x57)]/(1+7) = 440/8 = 55
Aw is thus maintained.

But, My Question is :

1. While changing the Weights (increasing / decreasing n1 & n2), the ratio in which they are mixed changes (from 1:3 to 1:7) . Is it okay that the mixing
ratio and thus the arm lengths changes,
to maintain Aw as constant ?



Next is, I decided to take an alternative view, by doing the reverse of what you said:
Assume that I increase the weight of the left pan by 3Kg (instead of 1kg as in the previous case) and decrease the
weight of the right pan by 1kg (instead of 3Kg as in previous case) as shown below:


                    3                           1
(A1)(40+3)-----------------(Aw=55)-----------------(60-1)(A2)
(59-55 = 4)                                            (55-43=12)
(n1 = 1)                                                      (n2 = 3)


This will become:

                    3                           1
(A1)(43)-----------------(Aw=55)-----------------(59)(A2)
(59-55 = 4)                                            (55-43=12)
(n1 = 1)                                                      (n2 = 3)

Computing Aw, I find it to be 55Kg
Aw = [(1x43)+(3x59)]/(1+3) = 220 / 4 = 55Kg

In this case:
2. The change in the weights, did not change the ratio in which they were
mixed and they did not change the ratio of arm lengths, but still maintained
the Aw as constant.


Which is right ? Have I understood something wrong ?
Could you please please please help me out ?? sad

Thirdly, you have also stated in the write up:
"If you want to keep the average same while changing weights in both the pans, the weights in the pan would be inversely proportional to arm lengths, i.e. to increase the weight in the left pan by one unit, we shall have to increase the weight in the right pan by three units to keep the average constant. Here, the arm lengths signify the distance of the weights from the average."

Shouldn't the second "increase" be "decrease" ? Because if one increases
from one side, the other side has to be reduced right ?

Lastly, you have stated:
"
the beam balance can also be represented with a beam balance of equal arms but one arm having thrice the weight on the other arm."

I don't get this statement too. Can you please explain ? sad


Sorry for the long post TG. Awaiting reply sad


Re: Average and Alligation
by sankar sattari - Friday, 18 July 2014, 06:07 PM
  to select 3 from 6 c(6,3)=20;
now its obvious that for all conc=50 so rule out (50,70,80)so ans= 20-5=15
Re: Average and Alligation
by Shivshankar Podder - Sunday, 8 November 2015, 06:10 PM
  Dear Sir
Kindly solve this question

1. Half of the volume of milk and water mixture of ratio 7:5 is converted into a mixture of ratio 3:1 by replacement method. The mixture of the ratio 7:5 was formed from the mixture 7:3 by adding water in it. If 240 L milk is required in the replacement method. What is the total amount of water was added to prepare the mixture of 7:5?

Options- a) 100 L b) 200 L c) 50 ml d) 400 L
Re: Average and Alligation
by Shivani K - Friday, 27 November 2015, 03:27 PM
  Hi Shivashankar,

is it 100L??