Alligation & Mixture (Basics) Video Lecture - Banking Exams

hi students today let's learn a very
important concept that is the concept of
allegation and mixture these are very
very important in sept
as it not only helps to solve the
questions quickly but it is helpful in
so many other chapters like average
percentage interest and ratios before we
proceed let's have a look on what all we
are going to cover in this session in
this session we are going to learn the
basic concept of allegation the
application of this concept in all the
other chapters then the concept of a
dilution by mixing the other content
repeatedly and lastly there will be a
few practice questions and answers for
your further development so first of all
let's learn the concept of allegation
let me take an example say in a class
the average age of boys happens to be 20
years the average age of girls happens
to be 15 years and the average of the
whole class happens to be 17 years the
students first important point to
remember is that the difference we need
to take in this case let me focus here
again we are talking about the word
difference the difference is something
which is always positive right so
difference basically means you subtract
the smaller number from the larger
number and the difference is to be
subtracted the way these lines are
indicating the Cross is indicating so
the difference of 15 and 17 - will be
written over here another difference of
3 will be written over here and that is
so happens to
to is to freeze another important point
students while deciding the ratio you
need to keep in mind that what is
written below what represents that
particular thing that is - happens to
appear below voice so that means the
ratio of boys to girls will be 2 is to 3
that is if there are two boys there are
three girls let us take one more example
say the average salary of years in a
company happens to be 20,000 the average
salary of females happens to be 15,000
and the every salary of the whole
organization happens to be 17,000
now you will take the difference
and then they are ratio so ratio comes
out to be two is two three four students
you should be careful about the point
here one the difference should always be
taken the way the lines are being drawn
and secondly it we are talking about the
word difference it's a positive value so
we always subtract the smaller number
from the larger number right now let's
move further to solve a few questions
just try to answer this first question
in this case the average marks of boys
are given to be 25 the average marks of
girls are given to be 40 and the average
marks of the whole class is given to be
30 so take the difference then five and
then you take the ratio the ratio
happens to be 2 is to 1 so this means
the ratio of boys to girls in this class
is 2 is to 1 right students now let's
move on to the next question this one
now here you are talking about two kinds
of rice their prices are given the price
of one kind of rice is given to be nine
point three the price of other kind of
rice is given to be 10 point eight and
the average price is given to be ten
rupees
so taking the difference here you get
0.8 taking the difference there you get
zero point seven cancelling with 0.1 or
dividing by ten that ways you can say
for that matter the ratio becomes eight
is to seven so this 8 is to seven she'll
become students the ratio in which we
shall be mixing the rice is worth rupee
9.30 and rise worth rupee ten point
eight zero respectively right let's move
to the next question this one now here
the ratio of milk and water is given in
two particular vessels you want to mix
to make it equal of milk and water now
here let us try to solve this question
firstly with the help of milk the
students what is the proportion of milk
in this proportion means the quantity
the ratio will given divided by the sum
of ratios what is the ratio of milk in
the second case it is 2/5 now you want
to mix these two to have half of the
total s make you took that half not take
the difference 2 by 5 taking the LCM to
be 10 4 5 it comes out to be 1 by 10
taking the LCM 14 this is 8 7 it comes
out to be 1 by 14 so reciprocating those
you get it as 14 and 10 and finally this
ratio happens to be 7 is 2 fights cry
students so the 7 5 becomes your answer
in this case now here let's solve this
question by way of
water if you take water as a common
point to start the proportion of water
in the first container is three by seven
water in the second container is three
by five
now those are to be mixed to have final
water as one by two take the difference
LCM again ten here you get one by ten
LCM 14 here you get 1 by 14 LCM 14 is to
10 ratio happens to be 7 is to 5 so
students you can very well see whether
you solve this question by way of water
or you solve this question by way of
milk the answer in any case is bound to
remain the same
it remains 7 is to 5 let's go to the
next question
in this question you have been given the
salary of clerks as 16,000 the salaries
of officers as 28,000 and the average
salary of those two categories as 20,000
so you take up the difference
and find their ratio which comes out to
be 2 is to 1 but is the question asking
that about the ratio from us
no the question is asking about how many
clerks are there so if you read
carefully the question has already
stated that there are 45 officers now
from here what we have got the
information what we have got the ratio
as that the ratio of clerks is to
officers happens to be 2 is to 1 and
question States there are 45 officers
students can I say if there is one
officer they are bound to be 2 clerks
when there are 45 officers the number of
clerks are bound to be 90 double of that
so this 90 becomes your unsub students
right now let's move on to the next
question
this one now here read carefully two
kinds of sugars have been bought at the
rate of rupees 8 and rupees 2 and then
those have been sold at rupee 6 and
there is a gain of 50% - students you
cannot compare apples with oranges you
have to have the same unit into the
consideration so in this first of all
your selling price is given to be rupees
6 and there is a gain of 50% so from
that you will calculate the cost price
by applying the basic formula SP in 200
by 100 plus profit percent and this
comes out to be
for rupees now here the question becomes
you have one sugar add rupees a kg other
is rupees to a kg when mixed you get the
average price as four rupees so we write
it here we write 2 here we write the
average price of four here then we take
the difference to four and then we find
the ratio as 1 is to 2 now this one is
to two shall become your answer students
so answer for this question shall become
one is to two let's move to the next
question this one now here you have milk
and water ratio given you want to take
some proportion of the mixture out and
you want to replace it with water so
that the resulting mixture has equal
proportions students now again this
question you can solve by way of milk or
by way of water but in this question you
have proportion now if I try to solve
this question by way of milk
how much is milk there in this in this
way sir the milk happens to be 3 by 4
now minded students you take that
mixture out and what you added in that
is water
now how much milk water has water has 0
milk in it right this 0 may surprise but
this is effect because what you are
putting in is water and what you are
comparing is milk as water has no milk
in it we took the quantity to be 0 and
finally you want it to be equal to 1/2
you take the difference you take the
difference the ratio comes out to be 2
is to 1 but minded students it's a
slightly different question question
does not ask about the mixture the
question asked about what proportion of
the mixture should be withdrawn so that
means whatever has been withdrawn same
has been replaced that is this one
portion which has been withdrawn and
replaced has been of proportion out of
total also so that means this one out of
this total of 3 has been taken out and
replaced so answer in this case shall
become 1/3 right students in order to
remove a little confusion that some of
you have got let's solve this question
by way of water also
now how much water is there in this
mixture initially it is one by four and
how much water you are putting in minded
you are putting complete water only so
in terms of proportion in terms of
fraction when it is all water it has to
be represented by the value 1 it is 1
the whole water now these are mixed
after withdrawing so that the ratio
happens to be 1 by 2 take the difference
take the difference and the ratio that
you generate is 2 is to 1 again students
this one portion which has been
withdrawn and replaced has been
initially a part of the total also so
that means 1 out of 3 has been taken out
and replaced so what shall become the
answer from that from there the answer
again happens to be 1/3 so whichever way
you solve this question you solve this
question by way of milk or by way of
water the answer remains the same let's
solve one more question
now here some quantity has been stolen
and replaced with water quite of the
same type as we did in the last case now
here you have stolen there was 60% wine
you steal some part of this and you
replaced it with water now how much wine
is there in the water
it is 0% and finally the result happens
to be there is 40% wine so you take up
the difference
40:20 the ratio happens to be 2 is to 1
now students even in this case then one
portion which is stolen and replaced has
been a part of the total which is again
3 per chance so that means again the
answer of this shall become that one
third of the total has been stolen and
replaced just for your better
understanding let's solve this question
by way of water also initially it was
60% wine so how much water was there it
was 40% now what you added there and you
added water so water means complete
water or 100% water and finally just
read it carefully there is 40% wine so
how much percent water is there it is
60% so you take up the difference you
find the ratio again students this one
portion that has been replaced has been
a part of this total 3 so what becomes
your answer your answer again becomes
1/3 only right student so in both the
cases you can see the answer remains
one-third only
let's go to the next question in this
question there is given to be 200 liter
mixture and there is 10% water now here
what we are adding in this in this we
are adding water so water will have what
percent water in it can I say water will
have 100 percent water in this and
finally we wanted to have 25 percent
water so we write 25 in between we take
up the difference can we find the ratio
which comes out to be 5 is to 1 now we
have been given a total of 200 liter
mixture which contains 10 percent water
sort of the two quantities mentioned
here on the top can I say this is given
to us as 200 litres so this is we need
to find so X shall become equal to 200
divided by 5 that is 40 meters so this
forty liters will become our answer as
students let's move to the next question
in this question it says a ratio of wine
and water a seven is to three and
finally this ratio might be reversed so
can I say you want to make this ratio as
three is to seven for wine and water now
again we can solve this question by
either of the two ways let's solve this
question by
of water now how much water is there
initially the water happens to be 3 by
10 in this what are you adding to this
you are adding to this water which means
complete water that is whole this is
water only so it will be represented by
one infraction now these two are mixed
so that there is 7/10 of the water then
you take up the difference T by 10 4 by
10 the ratio happens to be 3 is to 4 now
out of the 2 quantities here this 30
liter given to us belongs to what it
represents that part which has 3/10
water so can you say this 3 here becomes
30 liters so what will 4 become here can
you say it will be 30 divided by 3 into
4 or this 40 litre will become hi
students so this 40 shall be our answer
now let's learn a very important formula
this one now here this is a repeated
dilution formula when time and again you
repeat a dilution say you keep on adding
water in a wine or you keep on adding
some other quantity or other component
in or total this is where it works here
quantity left is equal to M then 1 minus
n by M raised to power T where m is the
total quantity n is a quantity withdrawn
and T is a number of times this has been
done the same formula can also be
thought of as
quantity left / initial quantity is
equal to 1 minus n by M raised to the
power T because so many times it is not
given in absolute value but in terms of
ratio and when it is defined in terms of
ratio in that case we can apply this
formula to represent the ratio of
quantity left divided by initial
quantity we will learn it better with
the help of an example this one now here
it is given that initially it was full
of wine and finally the ratio left is
wine to water is 36 is 213 so we can
think
quantity left - initial quantity is
equal to 1 minus n by M / H to the party
let's place values here now quantity
left of - 36 out of the total of 36 and
13 that is 49 is equal to 1 - 4 by M
raised to the power 2 let's move further
in this 36 by 49 which can be written as
spear of 6 by 7 is equal to M - 4 by M
square
cancelling the square students you get 6
M is equal to 7 M - 28 now here M comes
out to be 28 litres so this 28 litre
becomes your answer students right so
this way we take the ratio of quantity
left initial quantity our question
actually becomes very very simple right
before we end the session students let's
have a few practice questions for you
there are two practice questions for you
followed by two more questions these are
the four answers for these four
questions I hope you all have learnt
this concept which is a wonderful
technique to reduce the time that you
take to solve the questions of so many
other chapters thank you happy learning