Aptitude Made Easy – Problems on Percentages full series, Learn maths #StayHome

Summary

This 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

00:00

📚 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.

05:01

💼 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.

10:02

💸 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.

Keywords

💡Percentage

A percentage is a way of expressing a number as a fraction of 100. It is used to describe how one quantity relates to another in terms of a hundredth part. In the video, percentages are the central theme, with explanations of how to convert between fractions and percentages, and how to apply percentages to solve various mathematical problems, such as finding what percentage one number is of another.

💡Numerator

In a fraction, the numerator is the top number that represents the number of parts being considered. In the context of percentages, the numerator is referred to as the 'rate percent'. For instance, in the script, 'ten percent' refers to 'ten' being the numerator when considering the percentage in relation to the denominator of 100.

💡Denominator

The denominator is the bottom number in a fraction that represents the total number of equal parts into which the whole is divided. In percentages, the denominator is always 100, as it signifies 'per hundred'. The script emphasizes that the denominator remains constant at 100 in all percentage calculations.

💡Fraction

A fraction is a numerical representation of a part of a whole, expressed as one integer divided by another. The video explains how to convert fractions to percentages by multiplying by 100 and vice versa by dividing by 100. For example, converting 'one-fifth' (1/5) to a percentage results in 20%.

💡Aptitude Exam

An aptitude exam is a type of test that measures a person's natural abilities. In the script, aptitude exams are mentioned as a context where percentage problems frequently appear. The video aims to help viewers solve such problems quickly and efficiently for these exams.

💡Rate

In the context of the video, 'rate' refers to the percentage increase or decrease in a value. The script explains how to calculate new values after a certain rate of increase or decrease, using percentages to understand changes in quantities like salary or commodity prices.

💡Consumption

Consumption, in the video, refers to the quantity of a commodity or service used. It is a key component in the formula for calculating expenditure, which is 'rate times consumption'. The script discusses how changes in the rate or consumption affect the overall expenditure.

💡Expenditure

Expenditure is the total amount spent on purchasing goods or services. In the script, the relationship between expenditure, rate, and consumption is explored, particularly how to maintain constant expenditure when the rate changes by adjusting the consumption.

💡Salary Problem

A 'salary problem' is a common type of percentage problem where the script discusses how to calculate the difference in salaries when one person's salary is a certain percentage more or less than another's. It is used to illustrate the application of percentages in real-life scenarios.

💡Percentage Increase/Decrease

The script explains how to calculate the new value of a quantity after it has been increased or decreased by a certain percentage. This concept is crucial for solving problems related to growth or reduction in values, such as changes in salary or commodity prices.

💡Formula

A formula in mathematics is a concise way of expressing information in a logical manner. In the script, formulas are used to solve percentage problems systematically. For instance, the formula for calculating the change in area when length and breadth are increased by certain percentages is given as (a + b + ab/100), where 'a' and 'b' are the respective percentage increases.

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

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[Music]