Percentages

Introduction

The percentage is a very commonly used term, but there is the fact that most of us don't know! The percentage is a word that is derived from the french word 'cent,' which means 100 in french.

Percentage basically is essentially out of hundred. This means that we compare data and numbers revolving around the value “100”.

For example: If we have a class of 6 students (A1, A2, A3, A4, A5, A6) and these six students have appeared for the 12th board exams, then we can judge which student is good in studies by looking at the percentages of them.

StudentA1A2A3A4A5A6
Percentage78%82%86%68%95%92%

 

And now we can conclude that student A5 is the best out of these as the student has the maximum percentage of marks amongst all the students.

Did you know? Whenever you multiply any ratio with 100, it returns the percentage. But how?

Let’s take the help of the unitary method to know this.

Unitary Method: Whenever we have a situation where two variables move in a linear manner with respect to each other, then the unitary method comes into play.

Why not have an example to understand this method?

Example

Raju goes to the market and buys ten apples for rupees 30. How much will he pay for 15 apples?
Solution

let Y be the rupees you will pay for 15 apples,

Then,

10 apples = 30 Rs

15 apples = y Rs

Cross multiplying to equate;

10 X Y = 15 X 30

Y = 45

 

So, we will pay 45 rupees for 15 apples.

Let’s see how we can implement the unitary method in the percentage-based questions:

Example

8% of a number is 6000. What is the number?

Solution

Let the number be N,

Now,

If 8% of N is 6000

Then 1% of N will be 6000/8 that is 750.

And this results in 

100% of N being 750 X 100 = 75000

Hence,

Using the unitary method we can say that N = 75000

Now, as we have understood percentage so let's see the concept of the percentage change.

Percentage Change

The term percentage always occurs when we go from one number to another. But the basic structure of percentage change will only and only occur when we talk about the difference between two numbers

Let’s understand this with an example:

If we have a number x that is changing to y 
 

then the percentage change of x to y will be

 

Percentage change = (change / original value) * 100

 

 

Let's see this actual using numbers.

If we have two numbers, 40 and 60, and we are going from 40 to 60, then we will have the percentage change as follows:

Change = 60-40 = 20

Original value = 40

Then,

Percentage Change = (20 / 40) * 100 = 50%

The percentage is increasing by 50%

 

But if we have the same two numbers and the change this time is from 60 to 40 then the change is as follows:

Change = 40-60 = -20

Original value = 60

Then,

Percentage Change = ( -20 / 60) * 100 = -16.66%

Percentage is decreasing by 16.66%

 

NOTE: 1. In percentage change, there should always be two numbers. 

            2. we need to figure out which number is the original number.

Percentage Change Graphics

An important topic that is used in chapters like interest, profit, and loss, etc. So basically, when we use a graphical method for doing the percentage change, it is generally called percentage change graphics.

Basics of percentage change

  1. 100% of a number itself.
  2. 10% of a number shifts one decimal point on the number towards the left.
  3. 1% of a number shifts two decimal points on the number towards the left.
  4. 0.1% of a number shifts three decimal points on the number towards the left and so on.

 

      For Example:

      Let’s take a number N = 12345

      100% of the number N is 12345

      10% of the number N is 1234.5

      1% of the number N is 123.45

      0.1% of the number N is 12.345

 

This was simple, wasn’t it?

Now PCG generally has two structures,

Structure 1

Given the starting value and the ending value. We will have to calculate the following two things:

  1. Absolute Change
  2. % Change

 

 

Let's understand this taking the help of an example :

Example

Let’s consider 50 changing to 65

Then, 

Absolute change = 65-50 = +15. Absolute change is +ve that means an increase in the % change.

 

10% of the number 50 is 5, and the number 15 is three times the number 5, which means that the percentage is increasing by 30% ( 3 * 10% =30%).

 

Structure 2

  1. The initial value is given to us.
  2. Percentage change is given to us.
  3. Absolute change is what we need to calculate.
  4. And calculating the ending value as well.

Example

There is a number 50 that has to be increased by 30%.

 

Doing this problem by the unitary method.

50 is 100%

X is 130%

And now we can cross multiply and equate:

X = (50 X 130) / 100.

So, this kind of makes things complex Calculations can be tackled using percentage change graphics.

 

10% of 50 is 5. 30% increase means adding 5, 3 times. 5+5+5 = 15 i.e adding 15 in 50 so the ans is 65.

 

Problems on Percentage Change

Let’s see some good problems on Percentage change based on different topics.

Area and volume-based problem

Problem Statement

The length of a rectangle gets increased by 30%, and the breadth is decreased by 10%. What is the percentage change in area?

Solution

Area = L X B, and now it becomes a product change situation.

Assuming that the original area = 100.

 

Hence the total increase in the area of the rectangle is 17%

 

Expenditure and revenue problem

Problem Statement

The price of petrol goes up by 20%, and people reduce its consumption by 10%. What will be the % change in expenditure?

Solution

Price X consumption = expenditure

Let’s assume that the original expenditure = 100.

Now we have something like this in hand

Hence, we conclude that the total increase in the expenditure on Petrol is 8%.

 

Product Constancy

Whenever we end up with the changes in a series, we need to come back to the original value, and this is called product constancy. It is applied in a lot of aptitude questions directly.

Problem Statement

The price of petrol has gone up by 25%, and the consumption of Petrol is reduced such that the expenditure remains constant.

Solution

Price X Consumption = expenditure

Now let 100 be the original expenditure after the price and the consumption change. The expenditure should be back at 100.

After a 25% increment in the price of Petrol, our expenditure becomes 125. So, 125 should be reduced by 25 to keep expenditure constant. This means consumption reduces by 20%

A 25% increase in price takes place and offsets a 20% decrease in consumption to keep expenditure constant.

 

Since we have understood the percentage, lets take a look at some questions related to the topic, and let's see their solutions as well!

Some Important Questions

Problem 1: A shopkeeper selling tables reduces the price of tables by 20%, due to which he gets an increment of 60% in the sale. What is the percentage change in the revenue?

Solution

Price ×sale = revenue. Assume the original revenue = 100. Now the two arrows, one for price and the other, are for sale. 

Hence, there is an increase of 28% in the revenue.

 

Problem 2: Bob(B) gets 20% more marks than Aman(A), and Chaitanya(C) gets 50% more marks than Bob. Then how much % less than Chaitanya does Aaman get?

Solution

Let's Aman's marks = 100.

 

Coming back from Chaitanya to Aman, a drop of 80 on 180, i.e., 80/180 = 4/9. The fraction 4/9 is equivalent to 44.44%. Hence, Aman gets 44.44% marks less than Chaitanya.

 

 

Some frequently asked questions are present too! So let’s have a look at them as well and clear the frequently asked questions now.

Frequently Asked Questions

Question 1: How do we find the percentage?
On dividing the given value by the total value and then multiplying it by a hundred returns us the percentage as a result.

Question 2: what is percentage change?
The term percentage always occurs when we go from one number to another. But the basic structure of percentage change will only and only occur when we talk about the difference between two numbers.

Question 3: What is product constancy?
Whenever we end up with the changes in a series, we need to come back to the original value, and this is called product constancy. It is applied in a lot of aptitude questions directly.

Key Takeaways

This blog takes you around how to find Percentages in detail. With this done, you may now switch towards aptitude preparation from our Guided Path.

As we all know, aptitude actually is a very easy way to score in interviews, so topics like this can help you clear aptitude rounds of a lot of interviews.

If you wish to read more blogs on aptitude, you can find spectacular blogs here.
 

Happy learning!

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