Percentage Study Notes & Material - All Teaching Exam

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%

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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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