Percentage Formula, Percentage Calculator and Questions

Percentage: Introduction

Percentage: Percentage is a way of expressing a number as a part of 100. It is denoted by the symbol “%”. Percentages indeed serve as a valuable tool for expressing relative quantities and making comparisons, and they find application in a wide range of fields, including finance, economics, education, and competitive examinations.

In competitive examinations, the knowledge of percentages can be utilized to solve questions from different topics. Some of the direct applications of percentage can be seen in Average, Profit & Loss, Simple & Compound Interest, Time & Distance, Time & Work, Simplification etc. It can also play an important role in questions asked in Mensuration, Geometry and Trigonometry.

Percentage Calculator

In this article, we are providing the basic definition of a percentage along with the formula of percentage and percentage questions which helps you with a percentage calculator and increase your score in the government competitive exams. You can learn shortcut percentage methods, and formulas to solve the questions on this topic. To score good marks in any exam, it is necessary to have knowledge of the important topics and clear the basic concepts.

Percentage Meaning/ Percentage Definition

Percentage is a mathematical expression used to represent a fraction of a whole, usually denoted by the symbol “%.” It is a way of expressing a part or a portion of something in relation to the whole, typically out of 100. In other words, it quantifies how much one quantity or value represents concerning the total or the entire quantity.

The formula to calculate the percentage of a quantity in relation to the whole is:

Percentage=(Part/Whole)×100Percentage=(WholePart​)×100

Here’s what each component represents:

• Percentage: The result you’re trying to find, represented as a percentage value.
• Part: The specific quantity or portion you’re interested in.
• Whole: The total or the entire quantity.

How to Calculate Percentage?

Here we are providing some examples to give you samples of how to calculate percentages using the percentage formula. These questions will help you to understand the Percentage, and percentage formula using a percentage calculator.

Percentage Sample Questions

Example 1: There are 200 students in a class. Out of them, 90 are girls. Find the percentage of girls in the class.

Solution: We are given,

Total students in the class=200

Girls in the class = 90

Percentage of girls in the class = (Girls in the class⁄ Total no. of students) × 100

Percentage of girls in the class = (90/200)x100 = 45%

Example 2: The price of a $1.50 candy bar is increased by 25%. Calculate the new price.

Solution: We are given,

Price of the Candy= $1.50

Increase in the price of candy= 25% or 25/100

New Price of candy= Old Price + increase in price

New Price of candy= 1.50 +25/100

New Price of candy= 1.50 + 1.50 ×.25

New Price of candy= $ 1.875

Example 3: Radha earns a monthly salary of $1200. She spends $280/month on food. What percent of the monthly salary does she save?

Solution: Monthly salary of Radha= $1200

Salary saved by Radha = $(1200 – 280) = $920

The fraction of salary she saves = 920/1200

Percentage of salary she saves = (920/1200)×100 = 920/12 = 76.667 %

Example 4: There are two numbers. If the first number is 20% larger than the second number then by how much percentage is the second number smaller than the first number?

Solution: Let us assume that the numbers stated here are x and y respectively.

Let the value of y be 100. So, the first number that is 20% larger than y will be 120.

x = 120, y = 100

Now as asked in the question, the second number is 20 less than the first number. To arrive at the answer, we have to convert this into percentage.

Therefore, the required answer is = (20/120) X 100% = (100/6)% = 16.667%

Example 5: What is the cosine of 1/6th of a circle?

Solution: As we know, a circle represents 360 degrees and 1/6th of a circle will be 60 degrees.

In the question, we have been asked to find the cosine (or cos) of 60 degrees.

Hence the required answer is = Cos(60^o) = 1/2 = 0.50

Example 6: A rectangular plot of land with length 10 meters and breadth 20 meters is to be fenced.As of now only 40 % of the fencing has been completed find the length of the fence that is left to be laid around the plot.

Solution: Length of the plot = 10 meters Breadth of the plot = 20 meters.

So, the perimeter of the plot of land = 2 X (Length + Breadth) = 2 X (10 + 20) = 60 meters

Now, we have to calculate the remaining length of the perimeter that is to be faced i.e. (100-40)% = 60% of the fence.

The required answer is = 60% of 60 meters = 36 meters

Percentage Chart

A candidate who has the knowledge of common fractions and their values in percentage has a clear advantage over the competition as it can save him/her lots of time spent in lengthy calculations. The table below lists out some common fractions and their corresponding percentages.