Concepts of Percentage

Definition of Per Cent:

A Fraction having Denominator 100 is called a Per Cent & is denoted by symbol %.

# To convert the Fraction into Percentage

To convert a fraction into Percentage, multiply the fraction by 100 & put % sign.

For Eg: 4/5 à 4/5 * 100 = 80%

# To convert Percentage into a Fraction

To convert a percentage into a fraction replace the % sign with 1/100 & reduce the fraction to simplest form.

For Eg: 20% à 20/100 = 1/5

# To convert Percentage into Ratio

To convert a percentage into a ratio, first convert the given percentage into a fraction in simplest form & then to a ratio.

For Eg: 25% à 25/100 = 1/4 = 1 : 4

Important Concepts:

       1.      100% of a Number = Number itself
               For eg: 100% of 500 = 500
       2.      50% of a number = Half of the number

              For eg: 50% of 500 = 500/2 = 250
       3.      25% of a number = Quarter(1/4th) of the number or Half of 50% of the number

              For eg: 25% of 500 will be 500/4 or 250/2= 125
       4.      To find the 1% of a number, shift the decimal point by 2 place to the left.

               For eg: 10% of 500 will be 5.00
       5.      To find the 10% of a number, shift the decimal point by 1 place to the left.

              For eg:10% of 500 = 50.0
       6.      5% of the number is half of 10% of a number

              For eg:5% of 500 = 50/2=25
       7.      15% of the number = Sum of 10% and 5% of a number

             For Eg: 15% of 500=(10% of 500)+(5% of 500=50 + 2 =75 

Using the above methods now we can find the percentage of a number easily:

Example:    15% of 400 = ?

Step 1: Split the percentage term into 2 numbers that we can easily find the percentage of. 

                 We can split 15% into 10% and 5%

Step 2: First find 10% of 400 by shifting the decimal point to the left by 1 place.

                i.e 10% of 400=40.0

Step 3: Now find 5% of 400 i.e half of 10% 

                i.e 5% of 400=40/2 = 20

Step 4:  Now add both the results

                  we get, 15%+5%=40 + 20 = 60
                  Therefore, 15% of 400 = 60

Important Formulas:

        1)    Percentage Increase/Decrease:

   

      ·         If the price of a commodity increases by R%, then the reduction in consumption so as not to increase the expenditure is:
= [(R/100+R) * 100]%

      ·         If the price of a commodity decreases by R%, then the increase in consumption so as not to decrease the expenditure is:
=[(R/100-R) * 100]%

    

         2)    Population:

        If the Population of a town be P now & it increasing at the rate of R% p.a, then,

·         Population after n years =  P[1+(R/100)]^n  

·         Population n years ago = P[1+(R/100)]^n

        3)     Results on Depreciation

If the present value of a machine is P & it depreciates at the rate of R% per annum. Then:

·         Value of the machine after n years= P[1-(R/100)]^n

·         Value of the machine n years ago= P/[1-(R/100)]^n

        4)    If P is R% more than Q, then Q is less than A by
={ [R/(100+R)]*100}%

        5)    If P is R% less than Q, then Q is more than A by
={ [R/(100-R)]*100}%

Learn the Following Table for Fast calculations:

Fraction	Percentage
1/1	100%
1/2	50%
1/3	33.33%
1/4	25%
1/5	20%
1/6	16.66%
1/7	14.28%
1/8	12.5%
1/9	11.11%
1/10	10%
1/15	6.66%
1/20	5%
1/25	4%
1/30	3.33%
1/40	2.5%
1/50	2%
1/60	1.66%
1/75	1.33%
1/80	1.25%
1/90	1.11%
1/100	1%

By Using this Conversion Table we can convert Fraction into Percentage and Percentage into Fraction easily.

For Eg: To find 3/5 in %?

Solution:  As we have 1/5=20%

then, Multiply both sides by 3

i.e 1/5x3 = 3x20%

Therefore, 3/5 = 60%.