# Percentage, Study Notes, Material - All Teaching Exam

By Komal|Updated : September 14th, 2021

In this article, we should read related to the Percentage, Important for the CTET Paper-1 & 2. This article covers an important topic from the quantitative aptitude section that is-Percentage. These formulas and shortcuts will be helpful for your upcoming teaching exams.

### 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% =3/5x100=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%

### 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}%

### 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.

 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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## FAQs

•  The weightage of the Mathematics Section in the CTET Paper 1 & 2 is 30 marks.

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

• Almost 2 to 3 questions can be expected in the exam from the percentage topic.