Aptitude Made Easy – Problems on Percentages full series, Learn maths #StayHome
Summary
TLDRThis video script delves into the fundamentals of percentages, essential for aptitude exams. It covers basic concepts, such as converting fractions to percentages and vice versa, and memorizing common fractions' percentage equivalents for quick problem-solving. The script also addresses three common percentage problems: finding what percentage one number is of another, calculating increases or decreases in values, and understanding salary-related percentage questions. Additionally, it introduces advanced topics like expenditure rates, percentage changes in values, and area calculations for rectangles, providing formulas and examples to simplify the understanding of these concepts.
Takeaways
- 😀 Percentages are essentially per hundred, with the denominator always being 100.
- 📚 Understanding basic percentage concepts is crucial for solving problems involving percentages.
- 🔢 Converting percentages to fractions involves dividing by 100, and vice versa involves multiplying by 100.
- 💡 Memorizing fractions from 1/1 to 1/10 and their corresponding percentages can simplify solving aptitude test problems.
- 💼 Percentage problems often involve calculating a certain percentage of a given number, such as 33.33% of 180.
- 📈 When a value is increased by a certain percentage, the new value can be found by multiplying the original value by the factor representing the percentage increase.
- 📉 Similarly, when a value is decreased by a certain percentage, the new value is calculated by subtracting the percentage fraction from 1 and multiplying by the original value.
- 💼 Salary problems in aptitude exams often involve calculating what percentage one salary is less or more than another.
- 🛒 Expenditure problems typically involve calculating how changes in rate or consumption affect the total expenditure.
- 📦 The formula for calculating the overall change in value when multiple factors are increased or decreased is (A + B + AB/100), where A and B are the percentages of change.
Q & A
What does the term 'percentage' mean?
-The term 'percentage' means 'per hundred', with the denominator always being 100 in any percentage calculation.
How do you convert a percentage to a fraction?
-To convert a percentage to a fraction, you divide the percentage by 100. For example, 20% becomes 20 divided by 100, which simplifies to 1/5.
What is the fraction equivalent of 20%?
-The fraction equivalent of 20% is 1/5.
How do you convert a fraction to a percentage?
-To convert a fraction to a percentage, you multiply the fraction by 100. For instance, 1/5 becomes 20% when multiplied by 100.
What is the percentage of 3 out of 60?
-The percentage of 3 out of 60 is 5%, as 3 divided by 60 equals 0.05, and when multiplied by 100 gives 5%.
Why is it beneficial to memorize the fractions from 1/1 to 1/10 in terms of percentages?
-Memorizing these fractions and their corresponding percentages allows for quick calculations in aptitude exams, saving time and effort.
What is the result of 33.33% of 180?
-33.33% of 180 is 60, because 33.33% is equivalent to 1/3, and 1/3 of 180 is 60.
How can you find out what percentage one number is of another without using the elaborate method?
-If you know the fractions and their corresponding percentages by heart, you can directly calculate the percentage by using the fraction equivalent to the percentage you need to find.
What is the new value of X if X is increased by 20%?
-If X is increased by 20%, the new value of X is 120% of the original X, or 1.2 times X.
How do you calculate the percentage decrease when a value is reduced by a certain percentage?
-To calculate the percentage decrease, you subtract the percentage decrease from 100% and then apply this to the original value. For example, if X is decreased by 20%, the new value is 80% of X, or 0.8 times X.
What is the basic formula for calculating expenditure in terms of rate and consumption?
-The basic formula for calculating expenditure is Expenditure = Rate × Consumption.
If the rate of a commodity increases by 50%, by what percentage must consumption decrease to keep the expenditure constant?
-If the rate increases by 50%, consumption must decrease by 33.33% to keep the expenditure constant.
How can you find what percentage one number is of another when both are related to a third number by different percentage increases?
-Assume the third number as 100, calculate the other two numbers based on their percentage increases, and then find the percentage of one number in relation to the other.
What is the formula to calculate the overall percentage change when two values are increased by different percentages?
-The formula to calculate the overall percentage change when two values are increased by percentages a and b is (a + b + (a × b) / 100).
If the length of a rectangle is increased by 10% and the breadth by 20%, what is the overall percentage change in the area?
-The overall percentage change in the area of the rectangle is 32%, using the formula for overall percentage change when two values are increased by different percentages.
Outlines
📚 Understanding Basic Percentage Concepts
This paragraph introduces the fundamental concepts of percentages. It explains that percentages are a way of expressing a number as a fraction of 100, with the denominator always being 100. The numerator is referred to as the 'rate percent.' The paragraph also covers how to convert between percentages and fractions, emphasizing the importance of understanding this conversion for solving problems. Examples are provided to illustrate how to calculate what percentage one number is of another and vice versa. Additionally, the importance of memorizing common fractions and their percentage equivalents (from 1/1 to 1/10) is highlighted, as this knowledge can simplify solving percentage problems quickly.
💼 Percentage Problems in Aptitude Exams
This paragraph delves into common percentage problems that appear in aptitude exams, focusing on three main types of questions. The first type involves finding what percentage one number is of another, which can be solved by dividing the smaller number by the larger one and then multiplying by 100. The second type of problem involves calculating the new value of a number after it has been increased or decreased by a certain percentage. The explanation includes how to handle increases (multiplying by the percentage plus one) and decreases (subtracting the percentage from one and then multiplying by the original value). The third type of problem discussed is related to salary, where one person's salary is a certain percentage more or less than another's, and the goal is to find the percentage difference in their salaries.
💸 Advanced Percentage Problems and Applications
This paragraph explores more complex percentage problems, including those related to salary, expenditure rates, and consumption. It starts with a salary problem where one person's salary is a certain percentage more than another's, and the task is to find what percentage of one person's salary is less than the other's. The explanation involves converting percentages to fractions and using them to calculate the difference in salaries. The paragraph also discusses problems involving changes in expenditure rates and consumption, explaining how to maintain constant expenditure when the rate of a commodity increases. The formula for expenditure (rate times consumption) is used to illustrate how to adjust consumption to keep expenditure constant. Additionally, the paragraph covers problems involving the increase in two numbers and how to find the percentage of one number in the other, as well as the formula for calculating the change in the area of a rectangle when its length and breadth are increased by different percentages.
Mindmap
Keywords
💡Percentage
💡Numerator
💡Denominator
💡Fraction
💡Aptitude Exam
💡Rate
💡Consumption
💡Expenditure
💡Salary Problem
💡Percentage Increase/Decrease
💡Formula
Highlights
Basic concept of percentages explained as per hundred with the denominator always being 100.
Understanding how to convert percentages to fractions and vice versa, simplifying calculations.
Memorizing fractions from 1 by 1 to 1 by 10 for quick percentage calculations.
Solving aptitude test problems using basic percentage concepts to find what percentage one number is of another.
Concept of increasing a value by a certain percentage and finding the new value.
Method to find the percentage decrease in a value and its new resultant value.
Salary problems in aptitude exams involving percentage increases and decreases in salary.
Using the formula expenditure = rate x consumption to solve problems related to cost changes.
How to determine the percentage reduction in consumption when the rate increases to keep expenditure constant.
Solving problems involving percentage differences between two numbers in relation to a third number.
Understanding the formula for calculating the overall percentage change when multiple values are increased.
Applying the formula to find the percentage change in the area of a rectangle when length and breadth are increased by different percentages.
Practical application of percentage concepts in solving aptitude exam questions quickly and efficiently.
Importance of learning percentage-related fractions by heart for rapid problem-solving.
The significance of understanding both basic and advanced percentage concepts for various exam situations.
Encouragement to register on freshersworld.com for job opportunities and to subscribe to the channel for more educational content.
Transcripts
the topic that we are going to look
today is percentages before start
solving a lot of the problems in
percentages let us understand the basic
and basic concepts it's falling in
percentages so first the name suggests
per centage --is which is nothing but
percent which is nothing but per hundred
so your denominator will always be
hundred in a percentages that's what is
the plain meaning of percentages so what
do you call the numerator here numerator
we call it as rate percent so that's why
if you get something like ten percent or
something
this always calls your numerator metre
eight us ten percent 20 percent let's
all a couple of small problems
what is 20 percent just now we discussed
20 percent is nothing by 20 by hundred 3
is what percent of 60
they are asking three is what percent of
60 so 3 by 60 in two hundred which is
nothing but 20 fine so five percent 3 is
nothing but five percent of 60 this is
the basic concept in percentage you
should understand why are we dividing it
by hundred let's understand another
concept of fraction into percentages and
percentage into fraction so this next
concept is convert percentages into
fraction and fraction into percent it's
a very simple concept so in percentages
to fraction what do we do we divided by
hundred in case of fraction into
percentages we multiply it by 100 to
understand this concept
let's solve a simple problem what is the
fraction of 20% so they are asking you
to convert the 20% into fraction what do
we do it 20% is nothing but 20 divided
by 100 which is nothing but 1 by 5 so
20% we have converted into 1 by 5 here
fraction into percentages where we
multiply in 200 so they are asking us to
convert 1 by 5 into a percentage so what
do we do in 200 which is nothing but 20
percent so in this case we take 1 by 5
is convert
into 20% so if you see we have taken the
same question in both the cases this is
nothing but the vice-versa of that so
percentage into fraction we are
converting 20% into fraction which is
nothing but 1 by 5 here we are
converting fraction into percentages
which is nothing but 1 by 5 into 20 so
these are the basic concepts you should
know before solving the sums in
percentages so the second part is that
you should first memorize it from 1 by 1
to 1 by 10 so one way 1 is nothing but
100 1 by 2 is 50% 1 by 3 is 33.33% 1 by
4 is 25 1 by 5 is 20% 1 by 6 is 6
sixteen point six 6 1 by 7 is 14 point 2
8 and so on till 1 by 10 where this is
useful let's take a question you could
have find these questions a lot in lot
of aptitude examination they ask what is
33.33% of 180 so if you're a person who
didn't know any of this what you have to
do you have to just find the ELA break
method like thirty three point three
three divided by hundred into 180 this
is very elaborate method and it's very
time-consuming in case of an aptitude
exam so if you're a person who knows all
these table by by heart you were not
directly thirty three point three three
is nothing but 1 by 3 so 1 by 3 into 180
which is nothing but 60 so directly you
know it is 60 let's solve another
problem so they have asked is what is 14
point 2 8 of 350 so instead of taking
the elaborate method of fourteen point
two a divided by 100 into 350 you know
fourteen point two eight is nothing but
1 by 7 so directly will take 1 by 7 into
350 and it's nothing but 50 here so this
is the main reason of knowing these
things it's very simple to remember so
if you remember this most of the
percentage problems can be solved within
5 6 seconds so let us understand the
other three basic problems that you
might face in a percentages problem so
the first concept is X is what percent
or fine this is a very basic problem you
will see in any aptitude exam
this means it is nothing but X by Y of
100 let us take a simple example 50 is
what percentage of 100 so it is nothing
but 50 by
hundred in two hundred nothing but fifty
percent so let's go to the next concept
so the second type is nothing but X is
increased by certain percentage so find
the new value of x this is another
common simple problem that we face in
percentage how to do that let's say for
example X is increased by 50 percent you
know 50 percent is nothing but 1 by 2 so
it is increased by 1 by 2 which is
nothing but 3 by 2 of the x value let us
understand this concept with a simple
example
so X value they are given it as 200 it
is increased by 20 percent what is a new
value of X 20 percent is nothing but 1
by 5 so it's increased by 1 by 5 which
is nothing but 6 by 5 of X we know the
value of x is 200 so 6 by 5 into 240
just 240 so the new value of x is
nothing but 240 let us go to the next
type third type is nothing but X is
decreased by certain percent let's take
the same example let's take the X is
decreased by 50 percent you know that 50
percent is nothing but 1 by 2 what do we
do here in increase we added here we
have to subtract it so 1 minus 1 by 2 is
nothing but the same 1 by 2 of X so let
us understand this with an example
same example we are taking but here the
only change is x value is decreased by
20% so 20 percent is nothing but 1 by 5
so what do we do 1 minus 1 by 5 which is
nothing but Phi minus 1 4 4 by 5 of X so
4 by Phi of 200 which is nothing but 40
here and 160 so if the X is decreased by
20% the new value of x is nothing but
160 the topic that we are going to look
today is percentages and it is a part 2
part 1 of percentages we dealt about the
basic concept of percentages and then
the 3 type of problems that you will
face in a percentage problem following 2
that we are going to see a concept in
percentage is nothing but salary problem
this is a common type of problem which
you will see in an aptitude exam let's
get started so the first question is
carnage salary is 2
it wasn't more than ashok then what
percentage of Ashok salary is less than
condition so what they are given in the
question
carnage salary is 20% more is nothing
but 1 by 20 by hundred more than Ashok
so this can be re-written as 100 plus 20
by hundreds is nothing but 120 by
hundred a which can be written as K is
equal to 12 8n e so Kanishka is equal to
12 by 10 no fee so the question that
they have asked is what percentage of
Ashok salary is less than current so we
will write it in the form of a here a is
equal to 10 by 12 of K so initially
Ashok salary was 1 now we are going to
reduce it by 10 by 12 of K so 1 minus 10
by 12 which is nothing but 12 minus 10
by 12 which is nothing but 2 by 12 1
basics so as we know in the first part
of percentages I was telling you the
importance of learning the fractions
from one by one to 1 by 9 so 1 by 6 is
nothing but sixteen point six six so we
know that Ashok salary is sixteen point
six six percent less than Kanishka so
let's solve another problem to
understand this concept better so the
second question is similar to the first
one what they say a salary is 50% more
than B what percentage of B salary is
less than year so how we do it a salary
is 50% more which is nothing but 1 by 50
by hundred which is nothing but of B so
is equal to 150 by hundred of B which
can be rewritten as a is equal to 15 by
10 of B this can also be written as B is
equal to 10 by 15 of a so what they have
given in the question what percentage of
B salary is less than a so that's what
we have to find out now so how to find
this so B salary was initially 1 we are
going to protect it from 1 so 1 minus 10
by 50 which is nothing but 15 minus 10
by 15 nothing but 5 by 15 which can be
written as 1 by 3 so 1 by 3 is what 33
point three three percent so as we know
that be salary is 33.33% less than off
me
so in this concept we are talking only
about the salary problem similar way
they'll be asking like fifty percent
less than B in that case what he will do
instead of plus you will be putting a
subtraction sign here and do the same
way in which we did so this is a common
type of problem when you will face in an
amplitude exam topics that we are going
to look today is percentages so in this
video we'll be dealing with various
other concept of percentages which will
be useful for your aptitude exam so the
first concept we are going to talk about
this problem is very common where
they're going to ask about the
expenditure rate or conception let's see
how we can do it so we know the basic
formula expenditure is equal to rate
into consumption so we should know this
formula by heart so what's the question
the rate of the commodity is increased
by 50%
what percentage of consumption we have
to reduce so that their expenditure is
constant this type of problem you can
commonly see in the outer your exam
where either one of it is increased and
they will ask you how much percentage
has to be reduced so that everything
remains constant so let's get started
we know that expenditure is equal to
rate into consumption what they have
given in the question rate of the
commodity is increased by 50% so 50% is
nothing but 1 by 2 you know previous
videos if you have seen we have told
that the importance of knowing these 1x2
till 1 by 9 percentages in by heart you
should know this very by heart because
instead of wasting time you can directly
write it here so 50% is nothing but 1 by
2 so it is increased by 1 by 2 into what
percentage of consumption we have to
radio so that the next part of the
question so consumption is as such so
expenditure is equal to it can be
written as 3 by 2 R into C so there is
the equation that we have got so the
second part of the question what they
are asking what percentage of
consumption we have to reduce so that
the overall expenditure is constant here
the consumption is 1
correct so how we can make sure that the
expenditure also be same here you can
see the overall equation has been
increased by 50% it can be become equal
only if consumption become 3 by 2 of our
in to 2 by 3 of see where these gets
canceled and the original equation again
3 times so how do we do that
initially it was 1 now we are making
sure it becomes 2 by 3 so 1 minus 2 by 3
which is nothing but 3 minus 2 by 3
which is 1 by 3 1 by 3 is nothing but
what 33.33% so the consumption has to
reduce by 33.33% in order to make sure
the expenditure remains constant so hope
you understand how did we do that we
know that expenditure is equal to rate
into consumption rate we increased by 50
percent to make the overall equation
constant we know that we have to
multiply the equation by 2 by 3 so that
everything gets cancelled and becomes a
first equation so once it's done the
initial consumption was 1 now it has
been reduced to 2 by 3 so that 1 minus 2
by 3 is nothing but 1 by 3 1 by 3
directly we know as 33.33% and that's
how we found the value of this let's go
to the next question
so the next question that they've given
is two numbers are greater than the
third number by 25% and 20% respectively
so what percentage of first number is in
the second number so what we're going to
assume is the third number as 100 so why
they are given first number is greater
by 25%
so first is nothing but 25% of 100 is
nothing but 125 similarly the second
number is greater than by 20% so it
becomes 120 so we know the first number
second number and the third number so
what are they asking in the question
what percentage of first number is in
the second number first number is 125
divided by the second number is 120 and
the percentage of it 0-0 cancel 5 6 125
into 5 is 6 25 divided by 6 which is
approximately 1 or 4 percent so how did
we do that when you find these kind of
questions what do you have to do you
have to assume a single number as 100
and based on that you can find out the
other two numbers and once you know all
the three numbers you can easily find
the percentage of it let's go to the
next step so in the next sum we should
understand this formula here if a value
is increased by a person and B person
then the overall resultant value you
have to use this formula a plus B plus a
B by hundred so let's take an example to
understand this so length is increased
by ten person and breadth is increased
by twenty percent so they are asking you
to find the change in the area of the
rectangle so we know the value of a
which is 10 percent and value of B is
just 20 percent now just substitute it
in the formula a plus B plus a B by 100
is a formula so it becomes 10 plus 20
plus 10 into 20 by 100 so it becomes 30
plus 2 which is 32 so the percentage
change in the area of rectangle is
nothing but 32 percent you can come
across a lot of sum which can ask you to
find the change in the particular value
so what do we have to do is it very easy
to find out you can just remember this
formula to find the answer for that in
today's video we understood two concepts
one is finding the change in the value
of the percentage and the rate and
expenditure problem if you are a person
who's looking for a job kind register in
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