In this article we are going to cover Percentage. It is one of the intersting topics in maths that we use in our day to day talks or sometimes we are using it to express the probability of occuring something.Even a person who has nothing to do with maths understands it very easily and often use it.
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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 part and then calculate 15% of each part.
15 kg from first part and 15 kg from second one. Thus making it 30 kg.
Method 2 :
Total amount of rice = 200kg
15 % = 15/100
Therefore 200×15/100 = 30 kg
Shyam gets 30 kg 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 savings to expenditure is:
Savings ÷ Expenditure= 90% ÷10%
= 9/1
The simplest ratio. = 9:1
Ratio/fraction to Percentage Conversion : Savings + Expenditure = 100%
⇒ 9 parts + 1 part = 100%
⇒ 10 parts = 100%
⇒ 1 part = 10 %
Angela's Savings = 9 part = 9 × 1part = 9 × 10% = 90%
Angela's Expenditure = 1 part = 1 × 1 part = 1 ×10% = 10%
Or
Total earning = 9+1 =10
Savings = 9/10 × 100 = 90%
Expenditure = 1/10 ×100 =10%
To learn more about Ratio click here.
Tricks Related to Percentage
If a rider moving at a speed of 50 km/h increases its speed by 20% and then reduce its speed by 20% what is the net change in his speed
The Formula for Net % Change
= a + b +(a × b)/100
Net % change in his speed
= 20-20 -(20×20)/100
= - 4%
Net change in the speed = -4% × 50
= -2 km/h
Hence The speed of the rider decreased by 2 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.