Percentage Definition, Formula, Tricks and Examples

On this page you will read information about important chapters of Mathematics, Percentage.

We have shared information about Compound Interest on the previous page, please read it.

Let us read and understand the information on the definition of percentage on this page.

What is Percentage Called

The literal meaning of Percentage is per hundredth or hundredth or hundredth.

In other words, “Percentage is a Fraction whose denominator is 100 and the numerator of the fraction is called the rate of percentage, it is often represented by the % symbol.”

Example :- 10% means 10 out of 100. If a person spends 75% of his income, it means that he spends 75 out of 100 rupees.

If another person’s income is Rs 500 and he also spends 75%, then he spends 75% of Rs 500 i.e. Rs 375. This does not mean that he spends only Rs 75.

“Percentage is made up of two words per and shat which means ‘7% in every hundred’ means 7 in every hundred i.e. 7/100.

Therefore, this fraction whose denominator is 100 is called percentage and the numerator of the fraction is called the percentage rate.

It is often displayed by %, it has no units like Rs, meter, kilogram, liter etc.

Percentage Formula

1. Area of ​​rectangle = length × breadth
2. Area of ​​square = side × side
3. Volume of cube = side × side × side
4. Volume of cuboid = length × width × height
5. Volume of cylinder = πr²h
6. Volume of cone = 1/3 πr²h
7. Volume of sphere = 4/3 πr³

Converting Percentages into Fractions

35%	35	7/20
48%	48	12/25
72%	72	18/25
6.40%	64	4/250
80%	80	4/5

Converting Fractions into Percentages

14/5	4/5 × 100	80%
2/3	2/3 × 100	22/3%
7/10	7/10 × 100	70%
2/5	2/5 × 100	40%
7/4	7/4 × 100	175%

Converting Percentage to Decimal

18%	18/100	0.18
274%	274/100	2.74
47.60%	47.6	0.476
71%	71/100	1%

Convert Decimal to Percentage

0.18	18/100×100	18%
1.128	1128/1000×100	112.8

Percentage Questions

Q.1 If Ram’s salary is 10% more than Anjali’s salary, then by what percent will Anjali’s salary be less than Ram’s salary?
A. 100/11
B. 200/3
C. 51/7
D. 97/9

Solution : According to the question,
Percentage increase/decrease = (% / 100+%) × 100
= 10 / 110 × 100
= 100/11
Ans. 100/11

Q.2 If A’s income is 25% more than B’s income, then by what percent is B’s income less than A’s income?
A. 100%
B. 20%
C. 60%
D. 40%

Solution : According to the question,
Percentage increase/decrease = (% / 100+%) × 100
= × 100
= 10 / 110 × 100
= 100/11
Ans. 100/11

Ans. 20%

Q.3 By increasing the numerator of a fraction by 10% and decreasing its denominator by 10%, the new fraction is 2/5, then tell the original fraction or the old fraction?
A. 7/11
B. 12/23
C. 18/55
D. 29/7

Solution : According to the question,
(100 + 10) / (100 – 10) = 2/5
110/90 = 2/5
2/5 × 9/11 = 18/55
Ans. 18/55

Q.4 If the price of rice decreases by 10%, a moneylender will lose Rs. 450. I buy 5 kg more rice, tell me what will be its new price and old price?
A. 4
B. 7
C. 9
D. 11

Solution : According to the question,
New price = % / 100 × Rs / item
= 10/100 × 450/5
= 9

Ans. 9 rupees per kilogram

Q.5 Due to increase in the price of pressure cooker by 20%, its sales decrease by 50%, how much percent less or more income will a shopkeeper get than before?
A. 10
B. 40
C. 30
D. 20

Solution : According to the question,
(100 +_ %) × (100 +_%) /100,
= (100% – reduction)
(100 + 20) × (100 – 50) / 100
= (120 × 50) / 100
= 60
= 100 – 60

Ans. There will be a reduction of 40%.

Q.6 If there is a 25% reduction in the price of a fan, its sales increase by 40%. Tell by what percentage will the income of a shopkeeper increase or decrease?
A. 5%
B. 8%
C. 2%
D. 6%

Solution : According to the Question,
(100 – 25) × (100 + 40) / 100
= (75 × 140) / 100
= 35 × 3
= 105
= (100 – 105)

Q.7 If Ram’s salary is 10% more than Anjali’s salary, then by what percent will Anjali’s salary be less than Ram’s salary?
A. 100/11
B. 200/3
C. 51/7
D. 97/9

Solution : According to the question,
Percentage increase/decrease = (% / 100+%) × 100
= 10 / 110 × 100
= 100/11
Ans. 100/11

Q.8 If A’s income is 25% more than B’s income, then by what percent is B’s income less than A’s income?
A. 10%
B. 20%
C. 25%
D. 40%

Solution : According to the question,
Percentage increase/decrease = (% / 100+%) × 100
= × 100
= 10 / 110 × 100
= 100/11
Ans. 100/11

Ans. 20%

Q.9 By increasing the numerator of a fraction by 10% and decreasing its denominator by 10%, the new fraction is 2/5, then tell the original fraction or the old fraction?
A. 7/11
B. 12/23
C. 18/55
D. 29/7

Solution : According to the question,
(100 + 10) / (100 – 10) = 2/5
110/90 = 2/5
2/5 × 9/11 = 18/55
Ans. 18/55

Q.10 If the price of rice decreases by 10%, a moneylender will lose Rs. 450. I buy 5 kg more rice, tell me what will be its new price and old price?
A. 4
B. 7
C. 9
D. 11

Solution : According to the question,
New price = % / 100 × Rs / item
= 10/100 × 450/5
= 9

FAQ

Read More :
Discount	Profit and Loss	Simple Interest
Simplification	LCM and HCF	Compound Interest

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