Percentage is a fraction whose denominator is always 100. x percentage is represented by x%.

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If we have to find y% of x, then

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**Calculation of Percentage**

If we have to find y% of x, then### 1. To express x% as a fraction :

We know

x% = ^{x}/100

Thus 10% =

^{10}/100 (means 10 parts out of 100 parts)
=

^{1}/10 (means 1 part out of 10 parts)### 2. To express x/y as a percentage :

We know that^{x}/y = (^{x}/y× 100 )
Thus

^{1}/4 = (^{1}/4 ×100 )% = 25%
and 0.8 = (

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Multiply the number by the following factor

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Multiply the number by the following factor

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^{8}/10 ×100 )% = 80%###
**3. To increase a number by a given percentage(x%): **

Multiply the number by the following factor###
**4. To decrease a number by a given percentage(x%): **

Multiply the number by the following factor###
**5. To find the % increase of a number:**

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**6. To find the % decrease of a number:**

## Some Observation

### #1

If 20% candidate failed in an exam then observations are- 80% represent passed in exam
- 100% represent total appeared in exam
- (80%-20%) = 60% represent difference between passed and failed candidate in exam

### #2

If a number is increased by 25% then observations are

- 100% represent the old number
- 125% represent the new number.

### #3

Remember that Base in the given sentence (Question) is always 100%

Eg. Income of Ram is increased by 20%

In this sentence

100% - represent the income of Ram

20% - represent increment

120% - represent new income of Ram.

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**Remember it :**

1 = 100%

1/2 = 50%

1/3 = 33 1/3%

1/4 = 25%

1/5 = 20%

1/6 = 16

^{2}/3%
1/7 = 14

^{2}/7%
1/8 = 12

^{1}/2%
1/9 = 11

^{1}/3%
1/10 = 10%

1/11 = 9

^{1}/11%
1/10 = 8

^{1}/3%
1/13% = 7

^{9}/13%
25% = 1/4

6.25% = 1/16

125% = 5/4

150% = 3/2

200% = 2

350% = 7/2

### #4

**If of A is equal to y% of B then -****Example: -**If 10% of A is equal to 12% of B, then 15% of A is equal to what percent of B?### #5

**If A is more than B,****Example:**- If income of Ravi is 20% more than that of Ram, then the income of Ram is how much percent less than that of Ravi?### #6

**If the passing marks in an examination is P%. If a candidate scores S marks and fails by F marks then–****Example: -**Pankaj Sharma has to score 40% marks to get through. If he gets 40 marks and fails by 40, then find the total marks set for the examination?### #7

**If a candidate scores marks and fails by a marks while an another candidate scores y% marks and gets b marks more than minimum passing marks, then –****Example: -**Raj scores 30% and fails by 60 marks, while Rohan who scores 55% marks, gets 40 marks more than the minimum required marks to pass the examination. Find the maximum marks for the examination?### #8

**If due to decrement in the price of an item, a person can buy Kg more in y rupees, then actual price of that item -**

**Example: -**Ram can buy 5 Kg more sugar in rupees 100 as the price of sugar has decreased by 10%. Find the actual price of the sugar?

### #9

**If in an election, a candidate got of total votes cast and still lose by y votes, the total number of votes cast –**

**Example:**- In an election contested by two candidates, one candidate got 40% of total votes and still lost by 500 votes, find the total number of votes casted?

### #10

**If the population of a town is P and it increases or decreases at the rate of R% per annum then –**

**I. Population after ‘n’ years :**

**II. Population ‘n’ years ago :**

**Example: -**The population of a town is 352800. If it increases at the rate of 5% per annum, then what will be its population after 2 years and 2 years ago?

### #11

**If the value of a number is first increased by and again decreased by the net effect is always decreased by**

^{x2}/_{100}%**Example: -**The salary of a worker is first increased by 5% and then it is decreased by 5%. What is the change in his salary?

## Examples

### #1

Q. If the difference between 62% of a number and 3/5th of that number is 36. what is the number ?

Sol:

Let the number be x.

Then x × 62% - x ×

^{3}/5 = 36
x ×62% -x V 60% = 36 (60% = 3/5)

x ×2% = 36

x ×

^{2}/100 =36
x =

^{36 ×100}/2 = 1800### #2

Q. 40% of Ram's income Rs. 1200 Then Find

**75% of Ram's income ?****1/4 part of Ram's income ?****1/3 part of Ram's income ?**

**(1)**

40% = 1200 Rs.

75% = 1200/40 ×75 = 2250 Rs.

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**Trick : **1200 / 40 × 75 = Rs. 2250/-

**(2)**

40% of income = Rs. 1200

Then 1/4 part (i.e. 25% ) of Ram's

income = 1200/40 ×25

= Rs. 750/- Ans

**(3)**

40% of Ram's income

= Rs. 1200

i.e. 2/5 part of Ram's income

= Rs. 1200

Then total income of Ram

= Rs. 1200 ×5/2

1/3 part of Ram's income

= Rs. 1200 ×

^{5}/2 ×^{1}/3
= Rs. 1000 Ans.

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**Trick :**

^{1200}/

_{2/5}× 1/3

=

^{1200}/2 ×^{5}/3 = 1000