Introduction to percentages :

A percent means per hundred,percentage  is a way of expressing a number as a fraction of 100. The symbol used for percent is , "%",

Percentage is a relative term ,it is used to express how large/small one quantity is, relative to another quantity.  For example, 60% is equal to `60/100` , or 0.60. 

 

Formulas related to calculate percentages of numbers:

 

The percent symbole equalent to   `1/100`  = 0.01 , for example 35% of 300 can be written as (`35/100` ) × 300 = 105.

Formula to calculate percentage

  •    Percentage (%) = `("Given value") / ("Total value") xx 100`

 

Simple rules to find percentage of numbers 

To calculate a percentage of a percentage, make the percentages to fractions and multiply .

The easy way to calculate Addition in percentage (discount `x1` % + `x2` %):

      y = `((x_1+x_2)-(x_1 xx x_2))/100`

if the percentage is given and asked to find what is the amount that contirbutes of the total amount 

then  Value  =   `("Percent value") / (100) xx "Total value"`

 

Some Examples based on percentages of numbers:

 

It is very important to know what is the total value that corresponding to 100% to do problems on percentage 

 Ex 1 :  What is 20% of 30? 

 Sol:Step 1Here the Total value is 30 and the percentage is 20%

Use the above mentioned formula to find the value corresponds to 20% i.e  

Step 2:Value  =   `("Percent value") / (100) xx 100 `

Step 3:Value = `(20)/(100) xx 30` = `6`

so the 20% of the 30 is 6.

Ex: 2 There are 60 students in the class , and 24 of them are girls. What is the percentage of girls in the class?

Sol:Step 1: Here the total number of students in a class is 60 out of which 24 are girls

Stpe 2:To calculate percentage of girls in class use the formula

Percentage (%) = `("Given value") / ("Total value") xx 100`

Step 3:Percentage(%) of girls = `(24)/(60) xx 100`  = `40`

The percentage of girls present in the class is  40% .

 

Some points on percent changes:

  •  An increase of 100% in a quantity what is the final amount in terms initial amount

100% of initial + 100% of increase = 200% of initial , which means the quantity has doubled.

  • An increase of 800% means the final amount is 9 times the original (100% + 800% = 900% = 9 times as large).
  • A decrease of 60% means the final amount is 40% of the original (100% − 60% = 40%).
  • A decrease of 100% means the final amount is zero (100% − 100% = 0%).
  • In general, a change of x percent in a quantity results in a final amount that is 100 + x percent of the original amount (equivalently, 1 + 0.01x times the original amount).