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How to Solve Percentage and Some Percentage Problems

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Whether you’re in a class or just living life, knowing how to calculate percentages is a fundamental arithmetic ability. Percentages are used to make house payments and calculate tips and pay taxes on goods. Everyone needs to know this, how to solve the percentage. So if you are new to trying this, don’t worry; we’re here to explain this concept.


Students must understand how percentage calculations operate to pass tests, and they must assist in calculating the percentage of marks earned. Percentages have no size, and hence it is called a sizeless number. If we say 80% of a number, then it means 80 percent of its whole.


In this blog, we’ll discuss how to solve percentage and types of percentage problems.


Let’s start with the meaning of percentage.


A Percentage refers to a figure or ratio that can be written as a fraction of 100. If we need to find the percent of a number, divide it by the whole number and multiply by 100. The symbol “% represents it.”



  • 10% is equal to 1/10 fraction.
  • 75% is equivalent to ¾ fraction.


Bonus point:

              To calculate a percentage, we can use these tricks.


x% of y = y% of x

              Example: Prove that 20% of 40 is equal to 20% of 40.


             Solution : 20% of 40 = 8

                              40% of 20 = 8

             Hence, it is proved that x% of y = y% of x is equal.


How to solve the percentage of a number?

If you are also confused about How to solve percentage then you should follow these steps:-


To calculate the percentage of a number:-


P% of number = X

Where X is the required percentage.

If we removed the percentage sign, then we need to express the formulas as :




Let’s 10% of 70=X


X= 7.

Percentage problems


There are three types of percentage problems:

  • Find the ending number
  • Find the percentage
  • Find the starting number


  1. Find the ending number: To use a percentage calculation to find the ending number in a problem: “what is 50% of 25?”. If you have, have both the percentage and the whole amount that you find a percentage for this problem.


  1. Find the percentage: For a percentage problem, you need to find the percentage “what percent is 5 of 2?”. You will need to calculate in a percentage how much of 2 is part of the whole of 5.


  1.  Find the starting number: A percentage problem may ask you to find the starting number may look like this: “45% of what is 2?”. It is typically a more complicated equation but can quickly be resolved using the formula.

How to calculate the percentage change?


   A percentage change is a numerical value that denotes the degree of changes every time. The change in a given worth is expressed as a percentage change. The following is the formula for calculating percentage change:-


  • For a price or percentage increase       

[(New price – Old price)/ Old price] x 100


  • For a price or percentage decrease

[(Old price – New price)/ Old price] x 100


Some solved examples on a percentage


Examples1: Let a bag contain 2 kg of mangoes and 3 kg of oranges. Find the ratio quantities present and the percentage occupied by each.  


Solution: The number of mangoes and oranges in a bag can be compared in terms of their ratio, i.e., 2:3. 

The precise quantities can be expressed in percentages of occupied space, as follows:


Total quantities present = 5 kg 

Ratios of mangoes (in terms of total quantity) = 2/5

                                                                         = ⅖ x 100/100 

It is the ratio expressed per hundred,

1/100 = 1%


Percentages of mangoes = ⅖ x 100 = 40

Percentages of grapes = ⅗ x 100 = 60.


Examples 2: Out of two numbers, 40% of the greater number equals 60% of the smaller. If the sum of the numbers is 150, then the more significant number is?


Solution: Let us assume, more significant number be X.

                 Smaller number = 150 – X


 According to the question,

(40 x X)/ 100 = 60(150-X)/ 100

2X = 3 x 150 – 3X

5X = 3 x 150

X = 90.




The problems of percentages and how to solve percentages. Calculating percentage is a mathematical process to carry out. You won’t need to use a calculator every time you compute a percentage, but you may learn the formula and enter amounts to calculate mentally. A percentage is also used to express interest charged for loans and investments. Thus we hope that our blog will clear all your doubts regarding How to Solve Percentage.

Frequently asked questions (FAQs)


  1. How do I find the percentage of number 2?

Ans: To find the percentage of a number between two numbers, divide one number with the other and multiply the result by 100.


  1. What is the easiest way to calculate the percentage?

Ans: The way to figure out any percentage is to multiply the number of items in questions and by the decimal form of the percent.



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