Percentages & Profit Loss - 1 | CAT Preparation 2024 | Arithmetic | Quantitative Aptitude
Summary
TLDRIn this educational video, Ravi Prakash introduces the fundamental concepts of percentages, emphasizing their importance in arithmetic, calculations, and data interpretation. He covers the conversion of fractions to percentages, provides a series of fraction-to-percentage values, and explains how to apply these in various quantitative problems. Prakash also discusses the concept of 'multiplying factors' for quick calculations involving percentage increases or decreases, demonstrating how to simplify complex percentage problems into straightforward multiplications.
Takeaways
- ๐ The script is a lecture on percentages, emphasizing their importance in various mathematical and real-world applications.
- ๐ข It covers the conversion of fractions to percentages, using multiplication by 100 to find the percentage value of a fraction.
- ๐ The instructor provides a method to quickly calculate percentages by relating them to fractions and remembering key values like 1/2 equals 50%, 1/3 equals 33.33%, etc.
- ๐ The script mentions 'speed math' techniques for quick calculations, suggesting that viewers should watch related videos for a refresher.
- ๐ง Memorization is stressed for certain fractions and their corresponding percentages, such as 1/8 being 12.5% and 3/8 being 37.5%.
- ๐ The concept of 'multiplying factors' is introduced, which is crucial for understanding how to increase or decrease a number by a certain percentage.
- ๐ ๏ธ The 'multiplying factor' is explained as either 1 plus the fraction value for an increase or 1 minus the fraction value for a decrease.
- ๐ For decrease problems, the script shows how to use the fraction of the decrease as a multiplying factor by subtracting it from 1.
- ๐ Conversely, for increase problems, the fraction value is added to 1 to find the multiplying factor.
- ๐ The importance of understanding and memorizing these multiplying factors is highlighted for solving a variety of quantitative problems quickly.
- ๐ The lecture concludes by reinforcing the importance of mastering percentages for success in quantitative aptitude sections of competitive exams.
Q & A
What is the main topic of the video?
-The main topic of the video is percentages, covering their importance, basic concepts, and calculations.
Why are percentages considered an important topic in arithmetic?
-Percentages are important in arithmetic because they form the foundation for solving various problems, calculations, and data interpretation sets.
What is the relationship between fractions and percentages?
-Fractions can be converted to percentages by multiplying the fraction by 100. For example, 1/2 is equal to 50%.
What is the percentage equivalent of the fraction 1/3?
-The fraction 1/3 is equivalent to 33.33%.
How can you remember the percentage of 1/7?
-You can remember the percentage of 1/7 as approximately 14.28%, using the mnemonic '7 two fourteen fourteen two eight'.
What is the purpose of the 'multiplying factor' concept in percentages?
-The 'multiplying factor' concept helps in quickly calculating the result of increasing or decreasing a number by a certain percentage.
How do you calculate the multiplying factor for a decrease of 20%?
-To calculate the multiplying factor for a 20% decrease, you use the formula 1 minus the fraction value, which in this case is 1 - 1/5, resulting in 4/5.
What is the percentage of 1/19 when multiplied by 100?
-When 1/19 is multiplied by 100, it becomes approximately 5.26%.
How can you find the value of 37.5% of a number using the script's method?
-You can find the value of 37.5% of a number by recognizing that 37.5% is equivalent to 3/8 of the number and then multiplying the number by 3/8.
What is the significance of remembering specific percentage values in the script?
-Remembering specific percentage values helps in quickly solving various quantitative problems and is useful in different areas of arithmetic, including profit and loss, time and distance, and data interpretation.
How can you find the result of decreasing a number by 87.5% using the multiplying factor?
-To find the result of decreasing a number by 87.5%, you multiply the number by the multiplying factor, which is 1 minus the fraction value of the percentage, in this case, 1 - 7/8 or 1/8.
Outlines
๐ Introduction to Percentages
The script introduces Ravi Prakash, the instructor, and the topic of percentages, emphasizing its importance in arithmetic, calculations, and data interpretation. The instructor suggests watching 'speed math' videos for a strong foundation in percentages. Basic fraction to percentage conversions are taught, illustrating the process of multiplying fractions by 100 to find their percentage equivalents, with examples ranging from 1/2 to 1/19, highlighting the significance of memorizing these conversions for quick calculations.
๐ข Fractions and Percentages Conversion
This paragraph delves deeper into the conversion of fractions to percentages, providing specific examples and mnemonic techniques for remembering them. It covers fractions like 1/7, 1/8, and 1/9, and introduces the concept of approximation for more complex fractions. The importance of understanding these conversions for quick calculations in quantitative aptitude sections of exams is stressed, along with the idea of deriving new values from known ones.
๐งฎ Applying Percentages to Calculations
The script explains how to use the percentage values derived from fractions to perform calculations, such as finding what percentage of a number is represented by another number. It provides a series of examples, including calculating 37.5% of 640 and 18.75% of 176, demonstrating the process of breaking down percentages into their fraction equivalents and simplifying the calculations using known values.
๐ Understanding Multiplying Factors in Percentages
The concept of multiplying factors in the context of percentage increase and decrease is introduced. The instructor explains how to find the new value of a number after a certain percentage change by using multiplying factors, which are derived from the percentage's fraction equivalent. Examples are given to illustrate how to quickly calculate the result of percentage changes using these factors.
๐ค The Role of Multiplying Factors in Problem Solving
This section emphasizes the utility of multiplying factors in a variety of quantitative problems, including profit and loss, simple interest, mixtures, time and distance, and data interpretation. The instructor provides a method to determine multiplying factors for both increases and decreases, using the formula of 1 plus or 1 minus the fraction value of the percentage change, and illustrates this with examples involving different percentage decreases.
๐ Conclusion and Continuing Education
The final paragraph wraps up the video by summarizing the importance of understanding multiplying factors for quick and accurate calculations in various quantitative problems. The instructor encourages the viewers to continue learning and practicing with a variety of questions to solidify their understanding of percentages and their applications.
Mindmap
Keywords
๐กPercentage
๐กFraction to Percentage Conversion
๐กArithmetic Problems
๐กData Interpretation
๐กSpeed Math
๐กMultiplying Factor
๐กApproximation
๐กQuantitative Aptitude
๐กProfit and Loss
๐กTime and Distance
๐กMixtures
Highlights
Introduction to the importance of percentages in foundational arithmetic and data interpretation.
The significance of watching speed math videos to boost confidence in percentage calculations.
Fraction to percentage conversion method explained using multiplication by 100.
Memory aids for common fractions like 1/2, 1/3, and 1/4 and their percentage equivalents.
The concept of 'per 100' in percentages and its relation to the word 'century'.
Quick calculation technique for fractions like 1/7 and 1/8 by relating them to known percentages.
The strategy of connecting fractions to simplify percentage calculations, such as relating 1/12 to 1/6.
Understanding the unique value of fractions like 1/17 and 1/19 in percentage calculations.
The method of deriving percentage values from known fractions for complex calculations.
The importance of memorizing specific fraction-to-percentage conversions for quick problem-solving.
The concept of multiplying factors in percentages for quick calculation of increases or decreases.
How to find the percentage of a number using fraction multiplication, exemplified with 37.5% of 640.
Breaking down complex percentages into simpler fractions for easier calculation, like 18.75%.
The use of fraction series to simplify percentage calculations, such as the 12.5% series.
Techniques for approximating percentage calculations for tough fractions like 1/23.
The application of multiplying factors to quickly find results for percentage increase or decrease problems.
The final summary emphasizing the importance of understanding percentages for various quantitative aptitude tests.
Transcripts
[Music]
[Music]
hi everyone my name is ravi prakash and
welcome to first class of percentages
percentage is super important topic
every line i say every question i solve
so important in this percentage topic
right because this will build up your
foundation to solve all the arithmetic
problems all the calculations all the
data interpretation sets right
everywhere this percentage will help
okay i have to be very good at
percentages solving percentages
i hope you have watched speed man we
have watched those speed match videos
where we discussed how to do fast
calculation in percentages right so all
those things very important percentages
okay
so before percentages please watch those
uh speed match videos right further
boost up your
confidence in percentages okay so let's
start percentages one
first class of percentages right now see
here
first we will see
all the
fraction
fraction
to percentage conversion we should
remember it right fraction to percent is
conversion
like start starting from
one by one
obviously one by one is what one by one
is hundred percent
right one by two what is one by two
fifty percent
we should remember to 1 by 19 okay what
is 1 by 3
33.33 percent right what i'm doing
actually is any fraction
any fraction multiplied by 100 will give
me the percentage value
right so half into hundred is what fifty
so fifty percent okay one by three into
hundred so it is hundred by three what
is hundred by three thirty three point
three three
so when you multiply any fraction by
percent a hundred it becomes percentage
right because what is percentage means
percentages means per 100 percentages
means per 100 okay percent per cent
percent sentiments sent means 100 okay
so percent the sentence in century word
also century century contains cent right
so sent means hundred century means
hundred okay
so
again so do all this right now one by
four you can calculate you can remember
easily also right what is one by four
one by four into hundred is what one by
four into hundred twenty five percent
okay one by five and two hundred is what
twenty percent okay now one by six now
you can connect this now you can connect
it now what is one by six here you see
one by three half is one by six so what
is thirty three point three three half
sixteen point six six percent
correct now what is one by seven
so what is one by seven
so again now seven you can't connect
with the previous one because one by
seven it is right one by seven when you
multiply it by hundred it becomes
hundred by seven so i know seven
fourteen ja ninety eight and 2 is left
so 14 plus 2 by 7
is written by 14 2 by 7 but in decimal
right so 1 by 7 is approximately 0.14
1 by 7 is approximately 0.14 so 2 by 7
is approximately 0.28 you can remember
it
14.28 percentage
okay one by seven fourteen point two
eight percent easy to remember also
because seven two fourteen fourteen two
twenty eight
so it's easy to remember then one by
eight one by eight is what it is half of
one by four what is one by four twelve
four twenty five percent what is half of
twenty five twelve point five percent
one by nine again nine is not a prime
number you can easily connect with any
previous one 1 by 9 is what 1 by 9 is
one third of one one by three one by
nine is one third of one by three what
is one by three thirty three point three
three it's one third how much eleven
point one one percent
okay one by ten is obviously ten percent
which i should not write this okay one
by ten is ten percent one by ten
multiplied by hundred ten percent one by
eleven
again you solve like this one by eleven
into hundred so see 1 by 11 into 100 let
me write here
each step is so important right how to
calculate being making calculation here
your calculation making fast okay
1 by 11 in 200
ninety nine
so nine plus one by eleven is left this
is nine one by eleven in which fraction
and which fraction is plus sign is
hidden okay nine one by eleven so nine
one by eleven is what what is one by
eleven
one by eleven is approximately point
zero nine so it is how much it is nine
point
zero nine percent is okay now one by
twelve
so how much one by twelve one by nine
twelve is not a prime number and we can
connect with another any previous one
value so one by twelve is half of one by
six what is one by six
sixteen point six six percent okay half
of sixteen point six six percent eight
point three three percent what is one by
thirteen
one by thirty is what seven point seven
percent okay seven point seven percent
remember it one by thirteen is seven
point seven percent
seven point six nine to be exact but you
can remember seven point seven so
one by fourteen
what is 1 by 14 half of 1 by 7 14.28
half is how much 7.14 percent you
remember this value right remember is so
important till 1 by 19.
now 1 by 15.
now what is 1 by 15 it is one third of 1
by 5. it is one third of one by five
what is one by five twenty percent one
third of twenty percent how much
six point six six percent okay twenty by
three is six point six six one by
sixteen what is one by sixteen
it is half of one by eight what is one
by eight twelve point five twelve point
five half is how much six point two five
percent okay one by seventeen what is
one by seventeen so again remember here
one by seventeen is five point eight
eight
right you can sense this value actually
so one by this kind of value values
right when it gets tougher now or one by
17 and all so 1 by 17 into 100 if you
multiply so 1 by 17 into 100 how much it
is
so 17 6 java 1 0 2 so it is just
slightly less than 6 slightly less than
6 right because 17 into 6 is 1 0
slightly less than 6 5.8 percent this
kind of approximation you can do okay
now
1 by 18
1 by 18
it is 1 by 18 it is half of 9.09 sorry
it is half of 1 by 9 what is half of 1
by what is one by nine eleven point one
one what is half of eleven point one one
so eleven point one half is what five
point five five
what is one by nineteen
so one minute is what it is
five we remember five point two six
percent
see i'll discuss one by nineteen also
this
approximations you should understand
one by nineteen
when multiplied by hundred
it becomes nineteen five ninety five
5 is left because it is 100 here 5 plus
5 by 19.
now what is value of 5 by 19 so had it
been 5 by 20 so 5 by 20 was exactly 1 by
4 what is 1 by 4.25 right had it been
had it been
had it been five by twenty so five by
twenty is exactly one by four that is
point two five but it is five by
nineteen so five by deliver then five by
twenty is slightly more because
derivative is less so fraction is
slightly more so 0.25 slightly more
right so we're right here 0.26 that's
why
okay so what is one by 19 around 5.26
percent right this kind of
approximations you can make very
important this data very important okay
because this is only the unique table
right now we can again derive very
values from here and many questions we
can frame from here okay so very
important data
right okay now you should apply this
kind of funda you should apply this kind
of funda right when we when you say
suppose i want to calculate value of 1
by 23
okay so what is 1 by 23 now so again you
multiply by 100
23 into 4 is 92
8 is left 8 by 23 so again you can sense
here okay if it was 8 by 24 perfectly 1
by 3 that is 0.33
but it is 8 by 23 here that means little
bit more than 8 by 24 that means little
bit more than 0.33 so you can rewrite it
as 4.34
slight less than point slight more than
0.33.34 so it is 1 by 234.34 percent to
the right this kind of approximation you
should understand you should understand
this kind of approximations
okay i hope it is clear this part
okay now come to
next part here
so how to uh derive values from the
table right suppose now i'm writing all
those important values which are used
throughout the quant okay we will find
these numbers throughout the quant every
time okay
and it will be useful table only
so i hope you've written table in the
notebook okay
so see
12 suppose i need to find the value of
what is the
37.5
percentage
of
okay
of
640
so this is our table are you right 37.5
percent special number itself right so
again what is what is the series now you
see 37.5 so you see some you see some
0.5 in this series right you search for
some point five percent test you will
see that one by eight is twelve point
five percentage
right there's a whole series you should
remember just twelve point five series i
say twelve point five then the next
number is three by eight that is thirty
seven point five percent because twelve
point one by eight multiplied by three
so twelve point five multiplied by three
thirty seven point five then five by
eight okay let me write it here
okay because
very important date i am writing here
okay so
since 1 by 8 is 12.5 percent
that means
3 by 8 is
point 37.5 percent
okay what is five by eight
plus
twelve point five into five that is
sixty two point five percent
it is seven by eight
twelve point five into seven that is
87.5
this value should values you should
remember okay so if you remember things
will become very easy 37.5 percent that
means three by eight
three by eight of 640. you cancel it it
it
80 times what is 18 to 3 240
right so it becomes so easy to calculate
value of 37.5 percent of 640 very easy
to calculate the value okay now suppose
18.75 percent of
eighteen point seven five percent of 176
right now looks like a tough question
looks like a tough question is actually
not again if you get defunder from where
does 18.75 percent comes right you
directly see from here on itself okay
that is it is eighteen point seven five
is the half of thirty seven point five
right thirty seven point five half is
eighteen point seven five what is it
39.5 three by eight what is 18.75
percent
half of 3 by 8 that is 3 by 60
so if you get 3 by 16 so you can now
sense it okay 1 by 16 was
6.25 percent
so from here also i can connect
y 1 by 16 was 6.5 because 1 by 8 was
12.5
half of it so 1 by 16 6.25 6.25 into 3
6.25 into 3 is 18.75 percent right into
three so that means it is three by
sixteen so it becomes very easy job
becomes very easy right three by sixteen
into one seventy six you can cancel here
eleven times what is the answer answer
is thirty three such a beautiful
uh numbers these are right to directly
get the fraction value and just solve it
okay
so got to be familiar with this kind of
numbers okay 37.5 18.75 all the numbers
i will write right one by one okay see
how many numbers have covered here so
many numbers 87.5 62.5 37.5
18.75 other than the table right so this
is a very important concept okay now
83.33
of
of
uh 83.33 percent off now let's take any
number take 606.
again looks like a tough question but it
is not what is eighty three point three
three fifteen gonna connect right many
ways to connect eight three point three
three if you remember one by twelve is
eight point three three percent
this is ten eighty three point is 10
times of 8.33 right 10 times 1 by 12 10
times so 10 by 12
10 by 12 is 83.33 percent can cancel 10
by 12 how much it is 5 by 6
5 by 6
therefore
five by six is eighty three point three
three percent
one more thing you can do
right again two is just break this right
eighty three point three three percent
so problem is due to this decimal part
right 0.33 so see in in the table in
table where does 0.33 come in decimal
parts you can see it
33.33
okay so you can break this as you can
break this as 50
plus
33.33 percent
okay
fifty percent plus thirty three point
three three percent
what is fifty percent one by two what is
this one thirty percent one by three one
by two plus one by three how much five
by 6
that is 1 by 2 plus 1 by 3 is what it is
5 by 6
so 5 by 6
right so 5 by 6 is 83.33 percent
okay 5 by 6 is 83.33
what is the answer here
so
this value is ultimately right either
you go by 1 by 12 way or you go by just
breaking by breaking this numbers right
what is the value of 83.33 percent five
by six remain remember it very important
value 83.33
you will see lots of time this because
this kind of numbers in percentage and
and quantity so 5 by 6 of
606 in cancel 1 0 1 times
so 1 0 1 into 5 is what 5 0 5 so 5 0 5
is the answer
right so all these some very nice
numbers we are discussing okay next one
next one
43.75
off
right
43.75 percent of 352.
now what is this 43.75 percent again if
you see here
you can solve this like 43.75
okay
it is like 50 percent
minus 6.25 percent you can break like
this
50 percent is 1 by 2 6.25 is 1 by 16
okay so this is how much this is 7 by
16.
okay one similar number is
56.25 percent
okay so
it is 50
plus 6.25 percent
that is 1 by 2 plus 1 by 16 that is 9 by
16
so two important numbers here right
43.75
and 56.25 percent
right these numbers you'll see
by solving questions further in quant
okay so remember these values
7 by 16 9 by 16 okay so you can simply
solve it now this is how much this is
7 by 16 into 352 resolve it now 16 to
the 32
and 2
22 into 7 20 to 7 142 into 7 14 140 plus
14 154
so this is the answer
right so all these numbers you got to
remember okay now next thing we'll
discuss next thing
next thing will be
multiplying factor okay
multiplying factor
in
percentages
okay what is multiplying factor you see
see all these concepts we are doing and
doing small small problems but very
important problems right whole
percentage
will be used in throughout in profit and
loss sici whole arithmetic mixtures okay
time and distance time and work
everywhere some question numbers also
right everywhere
data interpretation everywhere
percentage is there so for sentence you
understand thoroughly every line you
will listen and you solve these
questions right we'll be doing lots of
good
good coverage of questions good variety
of questions in this okay but what is
multiplying factor right multiplying
factor as a name suggests by what factor
i should multiply
okay
by
what
factor
should we
multiply
this is the meaning of multiplying
factor right multiplying factor
so see here
suppose a number here is
see it will be used it is very useful in
this kind of question suppose
i give you a question 840 is a number
right
you have to decrease
87.5 percent decrease
what is the value
okay so in this kind of question it is
very useful right it's doing multiplying
factor so it is basically
one step up one step up right
one step up miss while solving we can do
that one step in mind and directly can
write and get the answer it will be
faster if you understand this right
see what is multiplying factor now so
if i solve for
it is n point five percent okay so let's
say a number is x let's say a number is
x
i am decreasing 20 percent on x
what is this result can write result as
okay x minus 20 percent of x is what
you'll write normally
x minus 1 by 5 of x
okay this becomes
x into 4 by 5 right and talking about
this x into 4 by 5 this is what i'm
talking about my multiplying factor
sorry my multiplying factor right x to
be decreased by 20
by what factor i should multiply 4 by 5
this is the multiplying factor right
similarly here also
x is decreased by 87.5 percent x is
decreased by
it is n point 5 percent by what factor i
should multiply so what is that 7.5
percent seven by eight so x minus seven
by eight of x i can write the discussion
last flight right it is n point five
percent is what uh uh seven by eight
twelve point five percent one by eight
it's in point five percent seven by
eight so the result result is x into one
by eight
this is my multiplying factor this is my
multiplying factor right by what the
factor i should multiply to get the
result so x being decreased by design
point five percent simply multiply by 1
by 8 so what is the answer here 840
decrease by 87.5 percent simply multiply
by one by eight
so eight eight sixty four so answer is
what answer is eighty sorry not editor
64 i'm sorry is 840 yeah okay
so
it is one zero five
so one zero five is the answer okay so
how to get this quickly okay they get
this funda in mind multiplying factor is
formed by
when you when you
do the operation when you do the
operation with fractions in a question
right suppose
this question so x minus twenty percent
of x so x minus one by five of x right
so i've done the all the operation here
x minus 1 by 5 of x what is 1
x into what is x you get a common so
once you take x as common when you break
this step you take x as common it
becomes 1 minus 1 by 5 right
so
always this x will become as common and
this is always one here also right here
also taken i have skipped this step but
what is it what if i write this step
here this step will look like x you take
common here so if you take x some common
1 minus 7 by 8
okay 1 minus 7 by 8 right
so this is 1 minus 7 by 8. what is the
value here 7 by it this value is 7 by 8
so since decreasing so 1 minus 7 by 8
okay since if it is increasing right if
something is increasing here you can see
if something is increasing for suppose
x is being increased by 25 percent
it's like x plus 1 by 4 of x it's like x
into 1 plus 1 by 4 it's like x into 5 by
4 this 5 by 4 is my multiplying factor 5
by 4 right what is this 1 plus 1 by 4 so
you see here what is 1 by 4 so 1 by 4 is
our
is our
25 value why 1 plus because
it is increasing
here 7 by 8 is our it is 10.5 percent
degrees why 1 minus because it is
decreasing here also what is one by five
one by five is our
twenty percent value why one minus one
by five because
decreasing so always you can we can
generalize it now that
to calculate multiplying factor
so multiplying factor is always
in case of increase
it is 1 plus the fraction value
in case of decrease
it is 1 minus the fraction value
okay so 1 plus fraction value and what
is multiplying factor multiplying factor
okay 1 plus fraction value
and
1 minus fraction value
always right so for one in one step if i
want to write here suppose
if i take example
um
37 point sorry
27 6 uh
648
if decreased by
37.5 percent
what is the result
i should directly write i should
directly write 648 into 5 by 8 is the
answer
and solve it right 8 into 81 but the
answer answer is 4 05 directly i should
do why it now why 8 for fixed 48 into 5
by 8
point because
percent thirty seven point five percent
it is what it is
three by eight degrees for three by
eight degrees what is the multiplying
factor for decrease one minus fraction
value so one minus three by eight that
is 5 by 8 should be the multiplying
factor
right so simply 6 48 into 5 by 8 simply
that's it right
in one step sorry one step solution okay
last slide we did this
okay 840
to be decreased by it is 10.5 percent
think in mind okay what is what is the
fraction value is 7.5 percent seven by
so seven by eight degrees so 840 into
what into
1 minus 4 degrees 1 minus 7 by 8 that is
1 by 8
that's it what is the answer answer is 1
0 5 cancel it 1 0 5
this 1 by 8 is the multiplying factor
right because 7 by 8 degrees means what
again what is multiplying factor seven
by eight degrees one minus seven by
eight is the multiplying factor that is
one by eight
that is one minus fraction value one by
seven by eight right so easy is so so
fast it is
so easy and so fast
okay
now see 1212 when
decreased by decreased by 83.33 percent
i said let's say let's this time
increase by
increase by 83.33 percent what i should
do
one two one two into now what is 83.33
percent fraction value five by six so
five by six increase five by six
increase what is the fraction value of 1
plus 5 by 6 increase so 1 plus fraction
now okay so 1 plus 5 which is 6 that is
11 by 6
11 by 6 okay cancelled 2 0 2 times so 2
0 2 into 11 right as it is 202 into 11
it is
how much tell me 11 22 is 22 and
11 into 20 is what
see 11 you get 2 02 into 11 how you can
break it 200 into 11
sorry 200 into 11 is 2200 and 2 into 11
is 22 so it is 20 to 22
that's it
is the answer right so why 11 by 6 again
same reason because 5 by 6 increase so
this 5 by 6 increase is equal to
multiplying factor of what 1 plus 5 by 6
that is
11 by 6 this is what ln by 6
so increase 1 plus fraction value
decrease 1 minus fraction value
okay
so we'll continue this initial video
thank you
[Music]
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