Average - Learn the Art of Balancing Video Lecture - Banking Exams

hello students today let's learn here
the concept of average and the
application of the same in so many
actual CAD questions and a few more
tough questions before we move on to the
questions let's understand what all we
are going to do in this session in this
session we are going to cover a few
basic and advanced concepts relating to
average average is basically an act of
balancing we will learn this through the
application in so many questions the
concept of weighted average and its
application then we are going to do some
actual cat questions how can you make
those questions as sitters and finally
there will be a few practice questions
and there are answers for your extra
practice now before we move on to the
questions let's understand a few basic
concept of average as you all shall be
knowing average is basically calculated
as sum of so many terms divided by
number of terms in short this is what
average is all about an important point
relating to averages is that if the
terms are at equal difference their
middle term becomes the average let's
take an example say you want to
calculate the average of 12 24 36 48 and
60 as you can see there there are five
terms now when there are five terms
which term shall become the middle term
in this case nominal term becomes the
third term and which is a third term
here students the third term is 36 which
shall become your answer so the middle
term becomes average when the terms are
at equal difference besides that
another basic but very very relevant
concept is if a constant term is added
in all the terms the average increases
by the same if the constant term is
subtracted from all the terms the
average decreases by the same similarly
if you multiply all the terms by a
constant the average also gets
multiplied and the same goes with the
division as well price trends now let's
move on to the questions where we will
apply those concepts starting with the
first question here just have a look at
this question here you have the average
temperature for three days again the
average temperature for three days and
out of those three days two days are
common and one day is separate now
students can we see here that earlier
the average is 36.5 and now the average
is 38.5 so there is an increase of two
in the average so what can be assumed
can I say that two has been added in all
the terms how many terms are there there
are three terms so when you add two to
Monday Tuesday and Wednesday when three
terms you add to what is the total
addition can I say the total addition
becomes six in this case no students
there is an addition of six and the only
uncommon day happens to be earlier there
was Monday and this time there is
Thursday right so this difference of
this addition of six degrees has come
because you have added Thursday and you
have excluded Monday or the temperature
on Thursday is six more than Monday now
moving on the question states the
temperature of Monday
is 6x7 or the temperature on Thursday so
students can I say here let the
temperature on Thursday be seven so that
the temperature on Monday becomes six
you can write x with that if you feel so
and there is a difference of X in this
case now as we discussed in actual sense
what is the real difference between the
two the real difference between the two
is six
that is Thursday is six more than Monday
so can we find the temperature on
Thursday students as a question asks us
if X happens to be six
what shall become the value of 7x it
shall become 7 into 6 that is 42 right
so this 42 becomes your answer students
right now let's move to the next
question in this question we will learn
the concept of weighted average and its
application how can you actually make
the questions look very very simple and
besides that we will learn what average
is act of balancing how do you apply
that let's solve this question students
here what you see that the number of
teachers in every case is given to be
200 300 100 and so on so 100 we can take
as redundant we can just ignore the
value 100 and focus on the other points
and he has given that the average of all
the t-shirts we want is rupees 100 now
let's do it by balancing the average as
a question specifies is already given to
be hundred now just focus on the first
part there are 200 teach
it's at 99.7 so I'll take their number
to be two and they are point three zero
less than the average so my net result
is minus of 0.6 then there are 300
t-shirts which will take as three and
they are point one zero more than the
average and our net result is positive
zero point three zero thirdly there are
100 tshis we'll take it as one with an
price of 100 point five this is zero
point five zero more net result is point
five more only right now one t-shirt
category number is missing but their
rate is given to be ninety nine point
nine five
so can I say they are - by point zero
five no students make sure firstly as
the average was given to be hundred and
we have taken that so net result has to
become zero now solving here negative
point six plus point 3 plus 0.5 what you
have to get here is a minus point two
zero whereas every term is minus point
zero five so how many terms are required
students I think you all can understand
you require four terms here and as we
already know 100 which was a constant
with all the terms for we will multiply
by 100 to conclude that the number of
t-shirts of this category shall become
400 now this 400 becomes your answer
right students let's move on to the next
question this one this is an actual cat
question wherein you have taken 10
two-digit numbers
and their average is increasing by 1.08
so as I told you when there is an
increase of 1.8 in the average we can
say 1.8 has been added to the first term
second term third term so on there are
10 terms so if you add one point eight
ten times there is a total addition of
18 and that is because you have just
interchanged the two digits and students
as you mathematically know if one number
is 10 X plus y and reversing will make
it 10 y plus X and if you take up the
difference between the two it is equal
to 9 times X minus y that simply means
whatever is the difference in the digits
9 times of that will be the difference
in the numbers and we have already
concluded in the numbers there is a
difference of 18 so that means what will
be the difference in case of digits it
will be 2 and see carefully this is what
your question is what is the value of B
minus a so uncertain this case will
become this to try students it seems a
very tough question but if you apply by
way of balancing by the basic of average
the question actually becomes very
simple let's move on to the next
question
this one measure care 2006 question now
for consecutive two-digit odd numbers
students if you take any consecutive
two-digit odd numbers say you take 11 13
15 and 17 you can very well
what will be their average it will be a
number which will be exactly in the
second and third term in between it will
be 14 so first point to with included is
that those four terms will have an
average of witches and even integer it
has to be even and it has to be integer
now when you divide it by 10 it becomes
a perfect square students can I say the
greatest two digit number is 99 so the
numbers are less than equal to that and
if you take four such numbers their sum
has to be less than equal to 396 and
mind it you are dividing it by 10 and it
becomes a perfect square so when you
divide it by 10 so that simply means
this unit digit has to be zero now let's
just think about perfect squares which
end with zero and they are less than 396
that is a perfect square
followed by a zero and it has to be less
than 400 so students will think about
the numbers these are 1 0 4 0 9 0 16 0
25 0 and 36 0 now moving on we will
solve this question by way of rejection
if we have taken four consecutive odd
two-digit numbers their average will be
an integer this visit total has to be
divisible by four but what you see here
the number 10 is not divisible number 90
is not divisible 250 is not divisible
and it has to be even if you divide it
by 4 the average comes out to be 10
the average comes out to be 40 and the
average comes out to be 90
right now here if you take the average
as pin can you say two of the numbers
have to be below 10 only but that is not
possible
so with that concept logic even 10 gets
nullified
now if 40 is the average can I say the
terms will be plus 1 minus 1 plus 3 and
minus 3 or if 90s average the terms will
be here plus 1 minus 1 plus 3 minus 3
now students because we solve this
question by way of concept now here the
number has to be one out of these eight
my date the question is very tricky as
you don't know the number is greatest
smallest or somewhere in the middle so
you need to find all and then you can
answer but conceptually it becomes a
real good question
try students let's go to the next
question
okay now let's solve this question a
cilenti question here see it says 10
years ago so we can say 10 years ago it
was a family of eight people and they
have a total age of 231 years
the students three years later it is
three years more than that or seven
years ago from the present can I say all
those eight people will be elder by
three months or there will be a total of
24 years addition now what happens
an elderly person of 60 year dies and a
child was born
now here plus 24 is due to this but at
the same time a person of sixty gets
expired and the child was born so this
means what is the net addition of those
two it is a decrease of 36 three more
years later or it is four years ago from
the present again the same scenario
happens so they all eight including the
child will be entered by three years so
plus 24 another persons of 60 dies same
process what is the net result minus 36
now what shall happen at present now
four more years or we are talking
exactly about the present scenario here
they all eight will be elder by four
years or there is an addition of 32 now
students what is the net result of all
these activities - 36 - 36 plus 32 it is
a decrease of 40 years now earlier the
total was 231 now you subtracted 40 from
this the net result is 191 years is the
total of 8 people again which tells you
that they are average
is approximately 24 years so this 24
becomes your try students now here if
you follow the process of X then it
happens then it gets added then
subtracted the question is going to take
at least three to four minutes now if
you solve it in this manner I think you
can solve the question very well within
one minute let's move on to the next
question
this one now here
this question is a very very important
question to learn the application of
weighted average now students here there
are 125 boys and there are 250 girls
what you have to do is straight away
they have their average weight given you
want to find the average weight combined
here you just need to focus on that the
ratio of boys and girls happens to be 1
is to 2 and your question is almost over
if there is one boy with the weight of
65 and there are two girls with the
average weight of 50 now this total of
165 is the weight of three people so
what becomes their average their average
becomes 55 yes
so this 55 here becomes your answered
students right so by this method we can
just ignore using the values like 125
250 wheresoever you have a number you
have a group of numbers which are in a
particular ratio just ignore the larger
values take their respective ratios that
way you can make your calculations quite
simple price range let's move to the
next question
this one now here teacher has written
all the consecutive natural numbers
starting from 1 up to how much is not
given student erases and you have been
given the new average now here first
thing you need to remember whenever you
take the average of n consecutive
natural numbers starting from 1 their
averages always n plus 1 by 2 so
students this question what you're going
to do is is a very different approach we
are going to apply but before we do that
let me revise one more formula with you
as I said average we all know is equal
to sum of terms divided by number of
terms here can I say whatever appears in
the denominator it is either the number
of terms or a factor of the same because
if there is a common factor and you
cancel that out the denominator will
become a factor of the number of terms
what I am hinting on is as in the given
question it is 35 7 by 17 so the
denominator has 17 this means the number
of terms are a multiple of 17 that is a
first hint to crack the question now
besides that the average is given to be
close to 35 no students as per the
formula we learned here that average has
to lie somewhere in the middle and it is
given to be 35 can I save 35 lies
somewhere in the middle what is the
number of terms whose average has been
taken that is close to the twice of 35
which is 70 now the number of terms are
close to 70 is the first hint that we
have generated and it's a multiple of 17
is the second hint that we have
generated can be clubbed the two
information students a multiple of
seventeen near 270 the only and only
possibility is 68 this means the average
of 68 terms have been taken but the
question talks about the numbers written
on the board initially we know when the
average is 68 terms is taken when one
terms is raised the total number of
terms before it was it is has to be 69
and sixteen nine terms becomes your
price to range here if you want to
calculate the number particularly which
was raised that you can also calculate
by applying the balancing thing which I
explained earlier try students now let's
move to the next question
this one here student is quite a
look-alike of a capture cat question now
here you have several subjects and the
marks are given to be in the ratio of 2
is to 3 is to 4 is to 5 is 2 6 6 to 7 is
to 8
can I say the terms are at equal
difference yes now which is the middle
term here the middle term is 5 so can I
safely take 5 to be their average and
students be careful the question says
his overall marks are 60% so can I say 5
is equal to 60% and now the question
tells you to compare for 75% and if you
see care
your question is almost over if 60% is 5
how much is 75% can we find that let's
do it if 60% is 5 how much is 75% you
cancel this you cancel 5 this is 4 it is
25 by 4 or 6 point 2 5 so students here
you can conclude that in terms of ratio
if in any subject he has six point two
five marks that means he is coring
exactly 75 but you want to know more
than 75 when how many cases the ratio
given is more than six point two five as
you can see there is seven and there is
eight so how many subjects are there
there are two subjects so in two
subjects he has poured more than 75
percent marks price range okay now let's
go to the next question
let's solve this question here let me
first of all tell you here that this 3 4
6 5 0 is actually redundant you do not
need this information to answer what is
important here is that on the way there
is 40% of the items which get damaged
now this 40% is very very crucial
students this 40% is how much in terms
of fractions we know 40% is equal to 2
by 5 so let's assume there are five
items in total why I am choosing 5
because the denominator is 5 that way my
calculations will actually become very
simple no students there are five items
as we assumed so out of that
two items were sold at a loss of 10% so
what is the net result it is minus 20
how many items are left three now this
is what we want to calculate but what is
the net result net result is that on all
the five items we want a profit of
twenty percent or they have to produce a
total of plus 100 and I can very well
tell you here you all can do balancing
net result you want is plus hundred here
there is minus 20 so what has to be
placed over here it has to be plus 120
over here price to range so fair has to
be plus 120 there are three items can we
find here that the average profit will
be equivalent to 120 divided by three
how much is that that is 40% rise to
range and this becomes your answer to
the question it's a wonderful way to
reduce any kind of calculations to a
very simple platform
had it been he says 33 one by three
goods we know it is one-third would have
taken the items to be three if he says
he says 37.5% we know it is three by
eight we will take the total goods to be
eight and so on
it has a universal application right
students now let's move and do one more
question this one is a 45 people class
their average age is given one boy
leaves again you need to find the
average on following first February it's
a tough question if you do by way of one
by one as a question is suggesting let's
do this question and make it really
simple in this case students forty-five
people their average is given to be
fifteen years and four months on first
of June now one of them leaves in
between
let me first assume he does not leave so
can I say that you want to calculate the
average on first of February which
appears after eight months of 1st of
June so everybody will be elder by 8
months or they will have an average of
16 years my students now had the person
not left that group of 45 will have an
average of 16 now the student actually
leaves on 1st October now had it been in
this group till date he would have been
elder by four months of Teuber numbered
December and January because we want
average on 1st February can you say when
he will be elder by 4 months his age is
given to be let me write it here 16
years and 2 months on 1st October so on
1st February he will be 16 years
six months four month elder no students
now I assume today he leaves today we
are talking on 1st of February and he
leaves where in the average of the whole
group is 16 years and the age of this
fellow is 16 years and 6 months can I
say he has those six months extra
because it's a part of those 45 when he
leaves then the six months that is extra
which we can write as 180 days he will
take equally among all the 45 people
because he is also a part of those 45
those six months or 180 days will be
taken equally from all the forty-five
students so everybody will contribute
four days if everybody will contribute
four days average will be less by four
days then the 16 years which we have
concluded if you subtract four days from
that the answer shall become 15 years 11
months and 26 days hi students if you do
this question by following the proper
method and channel the question actually
becomes very very lengthy right that's
it from our side I hope you all have
learnt whatever is being explained now
there are a few practice questions for
you in this case here is a first
practice question one more and two more
practice questions which you can solve
at your end so that you are able to
revise that concept apply whatever you
have learnt in this these are the
answers to these questions
I hope you all have enjoyed learning
average and you will be able to apply
that in the paper that you are going to
take thank you so much happy learning