Percentage:

By a certain percent we mean that many hundredths.
basically it means that if we are calculating x% of something it denotes the xth part of that product if we can divide it into equal hundred parts x percent means x hundredths written as x%.

Type-1:

To convert a percentage into fraction:

x%=x/100
e.g-60%=60/100=6/10=3/5

To convert a fraction into percentage:
x/y=x/y*100 %
e.g-3/5=3/5*100%=300/5%=60%

Type-2:
If a certain value a increased by x% then increased value=(100+x)% of a
e.g-50 increased by 20%
     = (100+20)% of 50
     = 120% of 50
     = 120/100*50
     = 6000/100
     = 60

If a certain value a decreased by x% then decreased value=(100-x)% of a
e.g-50 decreased by 20%
     = (100-20)% of 50
     = 80% of 50
     = 80/100*50
     = 4000/100
     = 40

Type-3:
Let the population of a town be X and suppose it increases at the rate of R % per annum,then

1.Population after n years= X*(1+R/100)^n
e.g- Population of town=100000
       R=10%
       Population after 2yrs = 100000*(1+10/100)^2
                                           = 100000*(1+1/10)^2
                                           = 100000*11/10*11/10
                                           = 12100000/100
                                           = 121000

2.Population n yrs ago = X/(1+R/100)^n
e.g-Population of town=100000
       R=25%
       Population 2yrs ago  = 100000/(1+25/100)^2
                                           = 100000/(1+1/4)^2
                                           = 100000/5/10*5/10
                                           = 100000*100/25
                                           =  400000

Type-4:
Let the present value of a machine be X and suppose it depreciates at the rate of R % per annum, then

1.Value of machine after n years= X*(1-R/100)^n
e.g- Value of machine=100000
       R=10%
       value of machine after 2yrs = 100000*(1-10/100)^2
                                                      = 100000*(1-1/10)^2
                                                      = 100000*9/10*9/10
                                                      =  8100000/100
                                                      =  81000

2.Value of machine n years ago= X/(1-R/100)^n
e.g- Value of machine=100000
       R=25%
       value of machine 2yrs ago = 100000/(1-25/100)^2
                                                      = 100000/(1-1/4)^2
                                                      = 100000/3/4*3/4
                                                      = 1600000/9
                                                      = 177777.78

Type-5:
If A is R% more than B, then B is less then A by - [R/(100+R) *100] %

If A is R% less than B, then B is more than A by - [R/(100-R *100)] %