Understanding percentages would help us with other mathematical concepts such as Profit & Loss, Simple Interest, Compound Interest and Data Interpretation where the questions are based on the concept of percentages. So, once you master percentages, you can easily solve problems from other mathematical concepts.
What Is Percentage?A percentage describes how many parts there are out of one hundred parts of a particular thing. When we say percent, we are actually saying “per cent” which means, ‘per hundred’ or ‘for every hundred’.
So, when we say 50%, we actually mean to say 50 per 100.
Percentage Defined As FractionPercent of something must make you think "divided by 100".
75% really means 75⁄100
12% really means 12⁄100
In the examples above, the denominator is always 100.
Hence, a percentage can also be defined as a fraction where the denominator is always 100 and the numerator is called rate percent.
Why Is The Concept Of Percentage Important?Example 1: Two kids appear for different exams, where student A scores 60, and student B scores 80. Since 80>60, it is easy to assume that B must be a better student than A.
However, let us now consider the total marks for each of these exams. Total marks in the exam that student A appeared for is, let’s say, 100 and that of student B is 200.
Student A scored 60/100
Student B scored 80/200, which in turn means he scored 40/100
Now, as (60/100) > (40/100), we can conclude that student A has fared better in his exam. Here, student A has scored 60% against that of student B who has scored only 40% in his exam.
We, thereby understand to never compare the performance of students with the actual marks but by the percentage of marks scored.
When we take into consideration performance of students in terms of the percentages scored, we make the scale common for all students, irrespective of the maximum marks scored.
Percentages are also used when calculating profit and loss. Hence, we use percentages to make the comparisons simple.
How To Calculate Percentage?Let us see how to convert a percentage into a fraction and vice versa:
Percentage to Fraction
Example 1: 50% = 50/100 = ½
⇒ 50% = ½
Example 2: 25% = 25/100 = ¼
⇒ 25% = ¼
Hence, to convert a percentage into a fraction, we need to divide the percentage value by 100.
Fraction to PercentageSimilarly, to convert any fraction into a percent, multiply the given value with 100.
Example 1: 3/8 * 100 = 37.5%
Example 2: 2/5 * 100 = 40%
What is Percentage Equation?
Example 1: 40% of 600 = 40/100 * 600 = 240
As you can see here, there are three types of values in the given equation:
- i. Percentage value: 40%
- ii. Maximum value: 600
- iii. Actual value/absolute value: 240
In a percentage problem when any two of these values are given, we can easily calculate the third.
Example 2: 60% of x = 360
Step 1: 60/100 * x = 360
Step 2: x = 6*100 = 600
Solution: 60% of 600 = 360
Example 3: x% of 900 = 720
Step 1: x/100 * 900 = 720
Step 2: x = 720/9 = 80
Solution: 80% of 900 = 360
Percentage ShortcutsLet us continue with Example 1 of the Percentage Equation = 40% of 600
Let us consider the maximum value to be 100, instead of 600
100% = 600
40% = x
Solution: By cross multiplication:
x = 40*600/100 = 240
In the method above, one of the percentage value is specified while you are required to find the other percentage. And that can be done by cross multiplying. With this method, we can solve the percentage problem quickly.
Example 1: 36% of 50 = 50% of 36 = 18 (which is nothing but half of 36)
How To Calculate Percentage Increase?
A’s salary = 40,000
Increased by 25%
A’s New salary = 40,000 + 25/100 * 40,000
= 40,000 +10,000
A’s salary = 40,000
Decreased by 20%
A’s New salary = 40,000 – 20/100 * 40,000
= 40,000 – 8000
If you understand these simple concepts of percentages well, you can easily solve problems from the quantitative aptitude section regarding percentages. With hard work and strategic practice, you could be one of the 2000 candidates to crack the bank exams.