entry removal of 1 element

[Aptitude] Averages: Entry / Removal of 1 element => Increase / Decrease inAverage Shortcut method explained

Situation: Entry of Element-Increase in Avg

Case: Avg age of Students + Teacher

Approach #1: convert into money problem1.Approach #2: Formula method2.

1.

Case: Avg salary workers+manager2.Case: Avg weight students+teachers3.Case: original average not given4.

1.

Situation: Entry of 1 element Decrease in Avg

Case: younger Kid joins: average goes down1.Case: Average Runs decline (original not given)2.

2.

Situation: Removal of 1 element -increase in avg3.Situation: Removal of 1 element -decrease in avg4.Mock questions5.

Situation: Entry of Element-Increase in Avg

Lets start with really simple case. In Gokuldham society, the average age of four kids is14 years. If Mr. Champak is included in this group, the average age increases by 11years. How old is Mr.Champak?

Convert this into money problem

Four kids got Rs.14 each.Champak makes a new gang with rule, everyone must have Rs.25 (bcoz14+11=25)But those kids got only Rs.14. so how much cash should Champak bring, to formthis new gang?

Lets think about it

Those kids got only Rs.14 each and want to join the new group.But each of them would need Rs.11 extra.So Champak must give them Rs. 11 x 4 kid = Rs.44And Champak also wants to be a part of this gang, so he should also bring Rs.25for himself.Therefore, Champak must bring Rs. 44 (to give to those kids) + 25 (for himself)=44+25=69Hence final answer: age of Champak is 69 years.

Mrunal [Aptitude] Averages: Entry / Removal of 1 element => Increase / ... http://mrunal.org/2013/02/aptitude-averages-entry-removal-of-1-element-...

1 of 8 7/28/2014 10:36 AM

Observe how numbers are moving while the average changes.

Case: Avg age of Students + Teacher

Average age of 36 students is 14 years. If teachers age is included, then averageincreases by one. Find the age of teacher. (RBI)

We can solve it by two approaches

Convert into Money problem (easy, quick)1.Formula method. (lengthy, time consuming)2.

Approach #1: convert into money problem

Whenever you face such question on average, try to convert it into a money problem,then it becomes very easy to visualize.

Converting into money problem

36 kids had Rs.14 each1 teacher comes.New average is 15 (original 14+ increases by 1)How much cash does teacher have?

Ok lets think about it.

There is a gang of 36 kids. And it has rule: everyone must have Rs.14.Teacher wants to form a new gang. And it has rule: everyone must have Rs.15.But those kids have only Rs.14 each.


2 of 8 7/28/2014 10:36 AM

So teacher must give Rs.1 to each of those 36 kids.Meaning teacher must bring Rs.1 x 36 =Rs.36And teacher should keep Rs.15 aside for himself. (because new gang rule iseveryone must have Rs.15)So how much cash did teacher bring in? =Rs.36 (to give to kids) PLUS Rs.15 (forhimself)=36+15=Rs.51 thats our final answer. Age of Teacher is 51 years.

Approach #2: Formula method

Formula for average: average = sum of observation divided by number of observation

Situation 1: without teacher

36=(sum of kids)/14Therefore, sum of kids(s)=36 x 14S=504

Situation 2: with teacher

37 =((sum of kids)+age of teacher))/15Therefore, S + teacher=37 x 15Now plugin the value of s=504 from previous equation504+teacher =555Teacher =555-504=51 thats our final answer.

As you can see, the problem with this formula method = youve to do lengthymultiplications (37 x 15 and 36 x 14). Thus

it breaks your momentum, decreases your speed in the exam.1.you might make some silly mistake in multiplications or during plugging thevalues in equations.

2.

So better just try to solve such questions using money problem method.

Case: Avg salary workers+manager

The average salary of 20 workers is Rs.1500. If managers salary is added, this averageincreases by Rs.100. Find the salary of Manager.(RRB)

It is already in money problem format.

20 guys have Rs.1500 eachNow Manager wants to increase this average by Rs.100. (new avg=1500+100=1600) So manager must give Rs. 100 to each of these 20 guys= manager must bringtotal 100 x 20 =Rs.2000 with him.But this new group has a rule everybody must have Rs.1600. Hence, If manager


3 of 8 7/28/2014 10:36 AM

wants to be part of this new group, he must keep Rs.1600 aside for himself.So, how much cash should manager bring? =Rs.2000 (to give to workers) +Rs.1600 for himself=2000+1600=3600 this is the final answer.

Case: Avg weight students+teachers

There are 24 kids in a class with average weight of 35 kilograms. If Teachers weightincluded, the average increases by 400 grams. Find weight of teacher.

Convert this into money problem

24 kids have 35 rupees each1.Teacher wants to form new gang: everyone must have 35.4 rupees each(because 400 gms =400/1000 kg =0.4 kg)

2.

Ok lets think about it

Teacher must give 0.4 rupees to each of those 24 kids=24 x 0.4 =9.6And he must bring Rs.35.4 for himself.so how much cash should teacher bring in? =9.6 (for kids) + 35.4 (for himself)=9.6+35.4=45. Thats our final answer: weight of teacher is 45 kilos.

Case: original average not given

In his 11th inning, a batsman scored 216 runs and his average increased by 12 runs.Whats his new average? (Bank)

Money problem

10 guys had Rs.m each1.

New guy (11th) has Rs.216 and he forms a new gang.2.In this new gang of 11 guys, each person has Rs.(m+12) each. Find value ofm+12.

3.

Lets think about it:

New guy wanted to form a new gang where everyone had Rs.m+12.But those 10 guys from old gang, had only Rs.mThat means new guy should give each of those 10 people Rs.12So new guy gave away Rs.12 x 10 =Rs.120So new guy is left with Rs. 216 (he originally had) MINUS Rs.120 (that he gaveaway)216-120=Rs.96 thats our answer.

so far we saw Average: Entry of 1 Element=>leading to Increase in Average.


4 of 8 7/28/2014 10:36 AM

Now lets check Average: Entry of 1 Element => leading to decrease in average

Situation: Entry of 1 element Decrease in Avg

Case: younger Kid joins: average goes down

The average age of six kids is 12 years. A new kid joins the gang and average decreasedby one year. What is the age of this new kid?

Money problem

Six kids got 12 rupees each.New kid wants to form a new gang with rule eachone must have only Rs.11


Since average is declining, we are sure that new kid has less money than Rs.11.But he wants everyone to have (12-1)=11 rupees.He tells those 6 kids, each of you give me 1 rupees. = 6 x 1 = Rs.6 borrowed.So how much money did that new kid bring? Well, Now he is part of new gang soobviously he has Rs.11 .but he has borrowed Rs.6 from others.Meaning, he originally had 11-6 =Rs.5Final answer: age of new kid is 5 years.

Lets try a case where one element is removed.

Case: Average Runs decline (original not given)

A cricketer made 90 runs in his 12th inning, and his average declined by 5 runs. Findnew average.

Money problem

11 guys had average Rs.m each

12th guy has Rs.90 and he makes new gang, with rule everyone must haveRs.(m-5)

Lets think about it

Since average is declining, we can be sure that new guy has less money than previous average (m).But he wants everyone to have (m-5) rupees (he should also have m minus 5rupees.)So he tells those 11 people, give 5 rupees each to me. = 11 x 5 = Rs.55How much cash does the new guy have now?= 90 (he originally had) + Rs.55(that he borrowed)=Rs.90+55=145 thats our new average.


5 of 8 7/28/2014 10:36 AM

Final answer: new average runs after 12 innings is 145.

Situation: Removal of 1 element -increase in avg

A batsman played 30 innings with an average of 78 runs.

If we ignore the score of his last innings, then average increases by 2 runs. How manyruns did he score in last inning?

Money problem

30 guys with Rs.78 each1 guy (Jethalal) leaves this gang after settling his debts.Average of remaining 29 guys is (78+2)=80 runs.

Ok lets proceed

Since average is increases after member leaves the gang= this member (Jetha) hadless money than others.That means other people had lended him some money (to raise him to the averageof 78.)When Jethalal leaves the gang, remaining guys get 2 rupees each.That means Jetha gave them Rs. 2 to each of those 29 remaining guys.=2 x 29=Rs.58And once upon a time, Jethalal was part of this gang, so he had Rs.78.It means Jethas original money = Rs.78 minus Rs.58 (that heborrowed)=78-58=Rs.20Final answer: batsmans score in last inning was 20 runs.

Situation: Removal of 1 element -decrease in avg

Four members of a family earn average Rs.7350. One of them, leaves and average goesdown to Rs.6500. How much did that person earn, who has now left the family? (SSC)

Money problem in our format:

4 guys with Rs.7350 each1.One of them (known as Jethalal) steals money from others and leaves.2.Now 3 guys left and theyve Rs.6500 each3.


Jetha wants to bring down average from 7350 to 6500 =decline of 850.So he must steal Rs.850 from each of the remaining three guys =Rs.850 x3=2550.And since Jetha was once part of this gang, he too used to earn Rs.7350himself.Therefore total cash with Jethalal =7350 (he originally had) + 2550 (that he stole)


6 of 8 7/28/2014 10:36 AM

=Rs.9900.

Final answer: the income of person who left family, is Rs.9900

Mock questions

Average age of 30 students is 11 .When teachers age is added, average increasesby 1 year. Find the age of teacher.

1.

Average of 24 wrestlers is 90. A new wrestler joins the gym and average increasesby 2 kilos. Find weight of new wrestler.

2.

Average annual income of 25 families in a society is 1.9 lakhs. A new familycomes to live in this society and the new average annual income of the wholesociety is increased by 10,000 rupees. Find the monthly income of this newfamily.

3.

Average salary of 21 workers+1 manager is Rs.2000. When managers income isnot considered, the average declines by 25%. How much does Manager earn?

4.

A batsman makes average 50 runs in 36 matches. After 37th match, his averageincreased by 1 run. How many runs did he score in last match?

5.

A batsman made 102 runs in 21st inning and his average increased by 2 runs. Findtotal runs scored by him in first 20 matches.

6.

A batsman scored 199 runs in his last match and his average increased from 44 to49. Find total number of matches played by him.

7.

A thief steals average 2 cars per night for 13 nights continuously. But after 14thnights adventure, his average increases to 3 cars. How many cars did he stealin that last night?

8.

Average salary of 21 workers is 2000. A new worker joins the company andoverall average declines by 2.5%. What is the salary of new worker?

9.

A batsman made average 80 runs in 29 matches. After 30th match, his averagedeclined by 2 runs. How many runs did he score in that last match?

10.

In a dance troupe, average weight of 20 junior dancers is 60 kilos. If the weight oflead dancer is also considered, the average declines by 500 gms. How much doesthe lead dancer weigh?

11.

In a society, average annual income of 30 families is 9 lakhs. One new familystarts to live here and average declines to 8.8 lakhs. Find the annual income of thisnew family.

12.

Answers

421.1402.4.5 lakhs annually / 12 = 37500 monthly income.3.Decline of Rs.500. So manager had Rs.500 x 21 + 2000= Rs.125004.87 runs.5.20 x 60 = 1200 runs.6.30 matches. he kept 49 for himself and gave 5 rupees each to m number ofpeople. 199=49+5m. so m=30 matches.

7.

16 cars. (Rs.3 for himself + 1 x 13 donated=16 cars stolen last night)8.2.5% decline= 50 rupees on 2000. so 21 workers gave him 21 x 50 =1050. and he9.


7 of 8 7/28/2014 10:36 AM

is part of new gang= he has 1950 minus 1050 borrowed =His salary is 900.20 runs.10.49.5 kilos.11.2.8 lakh.12.

URL to article: http://mrunal.org/2013/02/aptitude-averages-entry-removal-of-1-element-increase-decrease-in-average-shortcut-method-explained.html

Posted By Mrunal On 05/02/2013 @ 17:38 In the category Aptitude


8 of 8 7/28/2014 10:36 AM

entry removal of 1 element

Documents