## What is percentage ?

The word ‘per cent’ means per hundred, Thus ** x** per cent means

*parts out of 100 parts, this can also be written as . Therefore per cent is a fraction whose denominator is 100, and numerator of this fraction is called as rate per cent. Here*

**x****per cent is the rate and is denoted by the symbol**

*x***%**

Example:-

## Quick List of Formulae

- Any fraction if multiplied by 100 converts to a percentage (%)

% of any number*a*=*b*

is what % of*a*means*b*

- similarly,
is what % of*b*means*a*

- If a number
increases by**N**then it becomes but if*x%*decreases by*N*it becomes*x%*

- If a number or quantity
becomes*N*_{1}then percentage change = =*N*_{2}- if % change is
**(+) positive**then it is**% Increase**and if % change is**(-)****negative**then it is**% decrease**

- if % change is

- If a number changes by
% and then by*x*% the net change in % is =*y*

- If
is*A*more than*x%*, then*B***B**is =

- If
is*A*less than*x%*then**B,**is =*B*

## Conversion Methods

### 1. **Fraction to Rate Per Cent**

To convert any fraction to Rate Per Cent we need to multiply the fraction by 100 and put % sign.

Example:

### 2. **Rate Per Cent of a Number**

Rate per cent of a number is the product of equivallent fraction and the number.

value of rate percent =

Number =

** Example 1:** 25% of 1000 = =

**250**

** Example 2:** 9% of what number is 36 =

**3.** **Expressing a given quantity as a percentage of another given quantity**

** x** is what % of

**?**

*y*This question requires us to express one given quantity ‘** x**‘ as percentage of another given quantity ‘

*‘ since ‘*

**y****‘ is**

*y***the basis of comparison, so**, ‘

**‘ will be the**

*y***. hence the required percentage is =**

*denominator**Example 1 *:**30** is what percentage of **150** or what percentage of **150** is **30** ?

Here, ** x** = 30 ;

**= 150 Therefore, =**

*y*** Example 2:** What % of

**320**is

**128**

Here,** 320 **is the basis of comparison so **320** will be the **denominator, **therefore, the required percentage = .

**4.** **Percentage Change**

If a number or quantity increases or decreases to a new number then, ** % increase or decrease** = Here,

**original value**means the value of the number before

**increase**or

**decrease**.

** Example:** A man invested

**₹64,000**and

**₹80,000**respectively in the year 2018 and 2019. What is the percentage increase in the year 2019 from the previous year?

** Solution:** Required % increase = =

**5. Percentage Change and New Number**

If a number is **increased** by ** x%** then,

**New Number =**Similarly, if a number is decreased by

**then,**

*x%***New Number =**

** Example: ** The Current salary of a person is

**₹30000**& it has to be increased by

**20%**from next year. What will be the increased salary of the person ?

** Solution:** Here the salary increase = 20% therefore

**according to our formula % increase = = Hence the new salary will be**

*x= 20***₹36000**

**6. Two Step Change of Percentage**

If a number is changed by ** x%** in the first step and again changed by

**in the next step then the net change in percentage of the original number is If there is a decrease in any step then put a**

*y%***Minus (-)**sign before the number. And if the total change is

**Negative (-)**then the resultant number is decreased. and if it’s positive then the final change is Increased.

** Example:** If a number is increased by 20% and then decreased by 10% find the net change in the number.

** Solution**: Net change = Therefore,

**&**

*x = 20,***According to our formula: So the final increase will be**

*y = -10***8%**as our final result is

**positive**there will be a net increase in the original number.

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