A percentage is a fraction whose denominator is 100 and the numerator of the fraction is called the rate percent.
Percent is denoted by the sign '%'.
The term percent means for every hundred.

If we have to find x % of a number, then x % of number =	x	times of that number
	100

For example: 20% of 700 =	20	× 700 = 20 × 7 = 140
	100

Some fast result :-

10% of a number =	Number
	10

11.11% of a number =	Number
	9

12.50% of a number =	Number
	8

14.28% of a number =	Number
	7

6.66% of a number =	Number
	6

20% of a number =	Number
	5

25% of a number =	Number
	4

33.33% of a number =	Number
	3

50% of a number =	Number
	2

Example: Find 16.66% of 252.

Solution: 16.66% of 252 =	1	× 252 = 42
	6

Example: Find 14.28% of 504.

Solution: 14.28% of 504 =	1	× 504 = 72
	7

Example: Find 33.33% of 369.

Solution: 33.33% of 369 =	1	× 369 = 123
	3

Conversion of Percent into Number :-

To convert any percent into number we should divided by 100.

Example : Express 20% in fraction.

Solution: 20% =	20	=	1
	100		5

Example : Express 75 % in fraction.

Solution: 75% =	75	=	3
	100		4

Example : - Express 64% in decimal.

Solution: 64% =	64	= 0.64
	100

Conversion of Fraction into Percentage :-

To convert fraction into per cent we should multiply by 100 .

Example : Convert	3	into percent.
	5

Solution:	3	× 100 = 60%
	5

Example : Express 3¹/₄ in percent.

Solution: 31/4 × 100 =	13	× 100 = 13 × 25 = 325
	4

Expressing one quantity as a percent with respect to other .

Note : For this formula, both the quantity must be in same metric unit.
Example: 50 kg is what per cent of 250 kg?

Solution:		The quantity to be expressed in percent		× 100 %
		other quantity

=	50	× 100 % = 20%
	250

Example: 20 g is what per cent of 2 kg?
Solution: First quantity = 20 g and second quantity = 2 kg = 2000 g

∴		The quantity to be expressed in percent		× 100 %
		other quantity

=	20	× 100 % = 1%
	2000

Increasing percent and Decreasing percent :-

Example: Rent of the house is increased from ₹ 8000 to ₹ 10000. Express the increase in price as a percentage of the original rent.
Solution: Given, Initial rent = ₹ 8000 , New rent = ₹ 10000
Increase = New rent - Original rent
= 10000 - 8000 = ₹ 2000

Percentage increase =		Increase	× 100
		original value

Percentage increase =		2000	× 100 = 25%
		8000

Example: The cost of a bike last year was ₹ 50000. Its cost this year is ₹ 45000. Find the percent decrease in its cost.
Solution: Given, last year cost = ₹ 50000
This year cost = ₹ 45000
Decrease = Original cost - New cost
Decrease = 50000 - 45000 = 5000

Percentage decrease =		decrease	× 100
		original value

Percentage decrease =		5000	× 100 = 10%
		50000

Use of Percent :-

Trick: Successive change :-

where, A = first change and B = second change

Example: If the salary of a person increased by 10% of income. And again increased by 10% in next year. Find net percent change in his total salary.
Solution: Let A = 10% and B = 10%

Net percent change in salary = 10 + 10 +		( 10 × 10 )	= 20 + 1 = 21%
		100

Example: The price of an article is first increased by 20% and later on the price were decreased by 25% due to reduction in sales. Find the net percentage change in final price of article.
Solution:
Let A = 20% and B = -25%

Net percent change in final price = 20 - 25 +		{ 20 × ( - 25 ) }	= -5 - 5 = -10%
		100

10 % decrease in the price of an article.

Trick: To solve "Expenditure Constant" questions

where, x = increase or decrease
Use '-'sign for decrease

Example: Price of sugar is increased by 10%. Find by how much % the consumer should the consumption of sugar to keep the expenditure constant.
Solution: Here, x = 10%
Using the above given formula , we have

Reduction in consumption =		10	× 100 =	10	× 100
		100 + 10		110

Reduction in consumption =		100	= 9.09%
		11

Example: Price of rice is decreased by 20 %. Find by how much per cent the consumption should be increased to keep the expenditure constant.
Solution: Here x = 20%
Using the above given formula , we have

Increase in consumption =		20	× 100 =	20	× 100 = 25%
		100 - 20		80

Trick: If the population of a town is P and it increases ( or decreases ) at the rate of r% per year, then

Use '-' sign for decrement
Example: The population of a town is 472300. If it increases at the rate of 10 % per year, them what will be its population after 2 yr.
Solution:- given, P = 473200 , r = 10% , n = 2 yr

Population after 2 year = P			1 +	r		n
				100

Population after 2 year = 472300			1 +	10		2
				100

Population after 2 year = 472300			1 +	1		2
				10

Population after 2 year = 472300			11		2
			10

= 4723 × 11 × 11 = 571483

Trick: If the present population of a city is P and there is a increment or decrement of r₁%, r₂% and r₃% in first, second and third year respectively, then

Use'-' sign for decrement
Example: Population of a city in 2010 was 200000. If in 2011 there is an increment of 10%, in 2012 there is a decrement of 20% and in 2013 there is increment of 30%, then find the population of city at the end of year 2013.
Solution:- given, P = 200000, r₁ = 10%, r₂ = 20%, r₃ = 30%
Using above given formula ,

Population of city at the end of year 2013 = P			1 +	10			1 -	20			1 +	30
				100				100				100

Population of city at the end of year 2013 = 200000		×	11	×	4	×	13
			10		5		10

= 228800