# Percentage Formula

Mainly Percentage is used to denote part of hundreds as the name itself “per cent” suggests per hundreds. Some also defines percent as the fraction in which denominator is 100. The symbol which denotes percentage is %. Here we have given percentage formula.

**For Example:**

** **x% is x part of 100 i.e \(\frac{x}{100}\) .

40% is 40^{th} part of 100 i.e. \(\frac{x}{100}\) .

Also,

x% of y is y x \(\frac{x}{100}\)

50% of 10 is 10 x \(\frac{50}{100}\) = 5

**Formula To Express Percentage:**

[ \(\frac{quantity\: to\: be\: expressed\: in\: percentage}{quantity\: with\: respect\: to \:which\: percentage\:to\: be\: expressed}\) x 100 ]%

**Some of the amazing tricks about percentage:**

**1***. If the new value of some quantity is n times the previous given quantity, then the percentage increase is (n-1)100%.*

**Lets take an example**

If there is 2.42 times increase in your monthly salary then find percentage increment.

**Solution:**

Its simple

Percentage increment will be (2.42-1)x100% i.e. 142%

**2.** *If some value Y is increased by X% then New value will be Y(1 + \(\frac{x}{100}\) )*

**Example:**

Increase 50 by 20%= 50 {1+ \(\frac{20}{100}\)} = 50 x **1.2**= 60

**3.** **If some value Y is decreased by X% then new value will be Y(1 – \(\frac{x}{100}\) )**

**Example:**

Decrease 120 by 10%= 120 {1- \(\frac{10}{100}\)} = 120 x 0.9 = 108

**4.** **When compared what percent of X is Y then we use \(\frac{Y}{X}\) x 100%**

**Example:**

5 biscuits left in a packet of total 20 biscuits what is percentage of biscuits left in the packet?

**Solution:**

Percentage obtained is \(\frac{5}{20}\) x 100% = 25%

**5.** **When we have to calculate percentage change**

**Percentage change = \(\frac{change}{initial\: value}\) x 100%**

**Example:**

If the number of roses in a garland is increased from 50 to 60 then what is the percentage increment**?**

**Solution:**

Percentage change is \(\frac{60-50}{50}\) x 100% = 20%

*6. Term of successive Percentage Change*

*If there are successive percentage increment of x % and y%, the effective percentage increase is:*

*{(x + y + \(\frac{xy}{100}\))}%*

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