In this article we are going to cover Percentage. It is one of the interesting topics in maths that we use in our day to day talks or sometimes we are using it to express the probability of occurring something.Even a person who has nothing to do with maths understands it very easily and often use it.
.jpg)
This article has brought you a detailed overview to help you develop a strong conceptual grasp of this topic so let's begin.
What is Percentage
Etymologically percentage word is made up of two words Per + cent
Per means / (division)
Cent means = 100
Percentage : Anything that is taken out of 100. Let's understand it with some examples.
Example 1 : Suppose Ram got 100 kg rice, If Ram gives 15% rice to Shyam it means, out of 100 kg rice 15 kg rice is given to Shyam.
Example 2 : Angela's monthly salary is Rs. 100 and she expends 10% of her monthly income to charity
Angela expends Rs.10 in charity out of Rs.100.
Example 3 : john's car maximum speed is 100 km/h and he drives it with 50% speed.
His speed is 50 km/h out of 100 km/h
I hope you have got the basic idea about percentage Now it is time to slightly complex the level of examples
From example 1 Ram had 100 kg rice, now let's assume Ram has 200 kg of rice and he gives the same percentage (15%) rice to Shyam.Now the question is :
The amount of rice that Shayam gets is the same as before?
The answer to this question is No?
So let's see how much rice Shyam gets this time
There are two methods to solve it
Method 1 : Divide 200kg into two 100 kgs parts and then calculate 15% of each part.
15 kg from the first part and 15 kg from the second one. Thus making it 30 kg.
Method 2 :
Total amount of rice = 200kg
15 % = \( 15 \over 100 \)
Therefore 200×15/100 = 30 kg
Shyam gets 30 kg of rice.
Percentage to Ratio conversion and Vice versa
From Example 2 : Angela gives 10% of her salary to charity so she saves 90% of it.
So the ratio of her saving to expenditure is:
Savings ÷ Expenditure= 90% ÷10%
= \( 9 \over 1 \)
The simplest ratio. = 9:1
If the question is like the Saving and Expenditure ratio of Angela is 9: 1 then find Angela's percentage saving and expenditure.
Ratio/fraction to Percentage Conversion : Savings + Expenditure = 100%
⇒ 9 parts + 1 part = 100%
⇒ 10 parts = 100%
⇒ 1 part = 10 %
Angela's Saving = 9 part = 9 × 1part = 9 × 10% = 90%
Angela's Expenditure = 1 part = 1 × 1 part = 1 ×10% = 10%
Or
Total earning = 9+1 =10
Saving = \(9 \over 10\) × 100 = 90%
Expenditure = \(1 \over 10 \) ×100 =10%
To learn more about Ratio click here.
How To Calculate Percentage Increase and Decrease
Sometimes we have to measure the percentage change to analyse the progress,compare the values or how much a quantity has increased or decreased over a period of time. Let's see the formula how percentage change is actually calculated
Percentage Increase = \( {Increase \over \text{Original value}} \times 100 \)
Percentage Decrease = \( {Decrease \over \text{Original value}} \times 100 \)
Example 1 : Riya's monthly salary increased from $40,000 to $46,000. Find the percentage increase.
Increase in the salary = $46,000 - $40,000 = $6000
Original Salary = $40,000
Percentage Increase in
Riya's Salary = \( {Increase \over \text{Original value}} \times 100 \)
= \(\frac{6000}{40000} \times 100\)
= 15% increase
Example 2 : The population of a village decreased from 5,000 to 4,600. Find the percentage decrease.
Decrease in the population = 5,000 - 4,600 = 400
Initial Population = 5,000
Percentage Decrease in the Population
of the village = \( {Decrease \over \text{Original value}} \times 100 \)
= \( {400 \over \text{5000}} \times 100 \)
= 8 % decrease
Example 2 : The population of a village decreased from 5,000 to 4,600. Find the percentage decrease.
Decrease in the population = 5,000 - 4,600 = 400
Initial Population = 5,000
Percentage Decrease in the Population
of the village = \( {Decrease \over \text{Original value}} \times 100 \)
= \( {400 \over \text{5000}} \times 100 \)
= 8 % decrease
What is Successive Percentage change
When two or more percentage changes are applied one after another on the same quantity, It is referred to as Successive percentage change.
Each percentage change is applied on the value obtained from the previous percentage change.
Example 1 : Rahul’s salary increases by 20% and then by 10%. Find the net percentage change in his Salary.
Let Rahul's Salary = $100
First increase in his Salary = 20% of $100 = \( {20 \over 100} \times $100 \)
= $20
Rahul's Salary after first 20 % increase = $100 +$20 = $120
Second Increase in his Salary = 10 % of $120 (previous value)
= \( {10\over 100} \times $120 \)
= $12
Rahul's Salary after Second 10 % increase = $120+$12 =$132
Net Increase in Rahul's Salary = $132- $100 = $32
Initial Salary = $100
Each percentage change is applied on the value obtained from the previous percentage change.
Example 1 : Rahul’s salary increases by 20% and then by 10%. Find the net percentage change in his Salary.
Let Rahul's Salary = $100
First increase in his Salary = 20% of $100 = \( {20 \over 100} \times $100 \)
= $20
Rahul's Salary after first 20 % increase = $100 +$20 = $120
Second Increase in his Salary = 10 % of $120 (previous value)
= \( {10\over 100} \times $120 \)
= $12
Rahul's Salary after Second 10 % increase = $120+$12 =$132
Net Increase in Rahul's Salary = $132- $100 = $32
Initial Salary = $100
Percentage Increase in
Rahul's Salary = \( {Increase \over \text{Original value}} \times 100 \)
=\( {$32 \over \text{$100}} \times 100 \)
= 32% increase
Example 2 : The price of John’s mobile phone, which originally costs €10,000, decreases by 25% and then decreases by 20%. Find the percentage change in price of John's phone.
Initial Cost of phone = €10,000
First decrease in phone's price = 25% of €10,000
= \( {25 \over 100} \times €10,000\) = €25,00
John's phone price after first decrease = €10,000 - €25,00
= € 7,500
Second decrease in phone's price = 20% of € 75,00 (previous value)
= \( {20 \over 100} \times €7,500\)
= € 1,500
John's phone price after Second Decrease = € 7,500 - €15,00 = € 6000
Net Decrease in john's phone price = €10,000 - € 6000
= € 4000
Initial Price of phone = €10,000
Percentage Decrease in the price of Phone
= \( {Decrease \over \text{Original value}} \times 100 \)
= \( {€ 4000\over \text{€10,000}} \times 100 \)
= 40% Decrease
Initial Cost of phone = €10,000
First decrease in phone's price = 25% of €10,000
= \( {25 \over 100} \times €10,000\)
= \( {25 \over 100} \times €10,000\)
= €25,00
John's phone price after first decrease = €10,000 - €25,00
= € 7,500
Second decrease in phone's price = 20% of € 75,00 (previous value)
= \( {20 \over 100} \times €7,500\)
= € 1,500
John's phone price after first decrease = €10,000 - €25,00
= € 7,500
Second decrease in phone's price = 20% of € 75,00 (previous value)
= \( {20 \over 100} \times €7,500\)
= € 1,500
John's phone price after Second Decrease = € 7,500 - €15,00
= € 6000
Net Decrease in john's phone price = €10,000 - € 6000
= € 4000
Initial Price of phone = €10,000
Percentage Decrease in the price of Phone
= \( {Decrease \over \text{Original value}} \times 100 \)
= \( {€ 4000\over \text{€10,000}} \times 100 \)
= 40% Decrease
Net Decrease in john's phone price = €10,000 - € 6000
= € 4000
Initial Price of phone = €10,000
Percentage Decrease in the price of Phone
= \( {Decrease \over \text{Original value}} \times 100 \)
= \( {€ 4000\over \text{€10,000}} \times 100 \)
= 40% Decrease
Short Trick : If a rider moving at a speed of 50 km/h increases its speed by 20% and then reduces its speed by 20% what is the final speed of the rider ?
The Formula for Net % Change
= \( a + b +{a \times b \over 100}\)
Net % change in his speed
= \( 20-20 -{20 \times 20 \over 100}\)
= - 4%
Net change in the speed = -4% × 50
= -2 km/h
Hence The speed of the rider decreased by 2 km/h
The final speed of the rider = 50 km/h -2km/h = 48 km/h
The final speed of the rider = 50 km/h -2km/h = 48 km/h
Note : Here the Negative sign before speed indicates a decrease in the speed.
Percentage Questions with Illustrations
Here are some illustrations with hand written explanation
Illustration 1 : What is 20% of 50?
Illustration 2 : A pencil costs $40. If it is discounted by 10%, what is the discount amount?
Illustration 3 : What percentage of 100 is 25?
Illustration 4 : A class has 20 students and 5 are absent. What percentage of students are absent?
Illustration 5 : Ravi scored 45 out of 50 marks. What percentage did he score?
Percentage Worksheets
We have listed worksheets below based on the complexity. you can download them as pdf as per your requirements.