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 |
Thanks
Download the BYJU’S Exam Prep App Now.
The most comprehensive exam prep app
#DreamStriveSucceed
So why wait? Update your app right away!
Frequently Asked Question (FAQs)
Comments
write a comment