# Percentage Study Notes & Material – All Teaching Exam

By BYJU'S Exam Prep

Updated on: September 25th, 2023

Maths is an important subject in terms of all teaching exams. It is important to know all the important topics included in this subject. The percentage is among the important topic included in this section and candidates must prepare this section only with the best Percentage study notes.

In this article, we will read related to the Percentage, Important for the CTET. This article covers an important topic from the quantitative aptitude section which is Percentage. These formulas and shortcuts will be helpful for your upcoming teaching exams. Check the best Percentage Study Material here

### Percentage

• The percentage is the percent which means parts per hundred.

### Percent sign

• The percent sign is the symbol: %
• It is written to the right side of the number: 50%

### Percentage Definition

• The percentage is a value that represents the proportion of one number to another number.
• One percent represents 1/100 fraction.

If we have to convert the percentage into a fraction than it is divided by 100.

Example 1:‑ if we write 45% then it’s equal to 45/100 or infraction 9/20 or in decimal 0.45

If we have to convert the fraction into a percentage, we have to multiply with 100.

Example 2:‑ if we write 3/5 infraction, it is equal to 60% =3/5×100=60.

### Convert Percentage into Decimal:

• 20% = 20/100 = 0.5

### Convert Decimal Into Percentage:

• 0.25 = (0.25 × 100) % = 25%
• 1.50 = (1.50 × 100) % = 150%

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### Types of Formulas and Short Tricks

Type 1: Percentage Increase/Decrease:

• If the price of a commodity increases by R%, then the reduction in consumption so as not to increase the expenditure is: [R/ (100 + R)] x 100%
• If the price of a commodity decreases by R%, then the increase in consumption so as not to decrease the expenditure is: [R/ (100 – R)] x 100%

Type 2: Results on Population:

Let the population of a town be P now and suppose it increases at the rate of R% per annum, then:

• Population after n years = P(1 + R/100)n
• Population n years ago =P/(1 + R/100)n

Type 3: Results on Depreciation:

Let the present value of a machine be P. Suppose it depreciates at the rate of R% per annum. Then:

• Value of the machine after n years = P(1 – R/100)n
• Value of the machine n years ago = P/[(1 – R/100)]n
• If A is R% more than B, then B is less than A by= [R/ (100 + R)] x 100%
• If A is R% less than B, then B is more than A by= [R/ (100 – R)] x 100%

Note: For two successive changes of x% and y%, net change = {x + y +xy/100}%

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### Sample Questions with Solutions

Q 1. What is the quantity whose 9% is 18?

Solution:-  Let 9% of x = 18

x ×  = 18

or, x =

Q 2. What will be the effect on the area of a rectangle after decreasing its length and breadth by 20 and 25 percent respectively?

Solution:-  Percentage change in the area =

= – 45 +

= – 40%

Q 3. In a school 74 % of the students are boys. If the number of girls is 1235, then find the total number of students in a college?

Solution:- Percentage of girls

= 100% – 74%

= 26%

Let total number of students be x

According to question,

26% of x = 1236

x =

x = 4750

Q 4. Atul hides his income by 20% and tells it as Rs 6,000. What is the original salary of Atul?

Solution:- Original salary =

=

= Rs 7,500

Q 5. If 75 is added into 75% of a number, gets that number, then that number will be:-

Solution:-  Let the number be x

According to the question

This article tends to be beneficial for the following exams – REET, UPTET, CTET, Super TET, DSSSB, KVS etc.
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## Best CTET Books for Maths Preparation

It is important to include only the best books to prepare for the Mathematics section. Check only the best CTET Books as suggested by subject experts to prepare for the upcoming exam. Some of the books are mentioned below:

 Serial No. Book Name Author Name 1. Quantitative Aptitude for Competitive Examinations, Edition 7 R S Aggarwal 2. Mathematics Exam Goalpost for CTET & TETs Wiley Publication

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